Mixing
A game of probability
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An unbiased die having the numbers 1,2,3,4,5,6 is rolled 4 times. What is the probability that the minimum face value is 2?
According to my reasoning the answer should be $frac5^46^4$ because we have the options 2,3,4,5 and 6 . Which can be chosen for four trials in $5^4$ ways .
However the correct answer seems to be $frac5^4-4^46^4$ and I can’t reason it out. Please help me where I’m missing out
Thank you !
probability
asked 53 mins ago
Aditi
708314
add a comment |Â
up vote
1
down vote
favorite
An unbiased die having the numbers 1,2,3,4,5,6 is rolled 4 times. What is the probability that the minimum face value is 2?
According to my reasoning the answer should be $frac5^46^4$ because we have the options 2,3,4,5 and 6 . Which can be chosen for four trials in $5^4$ ways .
However the correct answer seems to be $frac5^4-4^46^4$ and I can’t reason it out. Please help me where I’m missing out
Thank you !
probability
asked 53 mins ago
Aditi
708314
$(5/6)^4$ is the probability that the minimum face value is $ge 2$.
– ncmathsadist
51 mins ago
@ncmathsadist so do you think that my answer is correct ? Please help
– Aditi
50 mins ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
An unbiased die having the numbers 1,2,3,4,5,6 is rolled 4 times. What is the probability that the minimum face value is 2?
According to my reasoning the answer should be $frac5^46^4$ because we have the options 2,3,4,5 and 6 . Which can be chosen for four trials in $5^4$ ways .
However the correct answer seems to be $frac5^4-4^46^4$ and I can’t reason it out. Please help me where I’m missing out
Thank you !
probability
asked 53 mins ago
Aditi
708314
An unbiased die having the numbers 1,2,3,4,5,6 is rolled 4 times. What is the probability that the minimum face value is 2?
According to my reasoning the answer should be $frac5^46^4$ because we have the options 2,3,4,5 and 6 . Which can be chosen for four trials in $5^4$ ways .
However the correct answer seems to be $frac5^4-4^46^4$ and I can’t reason it out. Please help me where I’m missing out
Thank you !
probability
probability
asked 53 mins ago
Aditi
708314
asked 53 mins ago
Aditi
708314
asked 53 mins ago
Aditi
708314
asked 53 mins ago
Aditi
708314
asked 53 mins ago
Aditi
708314
708314
$(5/6)^4$ is the probability that the minimum face value is $ge 2$.
– ncmathsadist
51 mins ago
@ncmathsadist so do you think that my answer is correct ? Please help
– Aditi
50 mins ago
add a comment |Â
$(5/6)^4$ is the probability that the minimum face value is $ge 2$.
– ncmathsadist
51 mins ago
@ncmathsadist so do you think that my answer is correct ? Please help
– Aditi
50 mins ago
$(5/6)^4$ is the probability that the minimum face value is $ge 2$.
– ncmathsadist
51 mins ago
$(5/6)^4$ is the probability that the minimum face value is $ge 2$.
– ncmathsadist
51 mins ago
@ncmathsadist so do you think that my answer is correct ? Please help
– Aditi
50 mins ago
@ncmathsadist so do you think that my answer is correct ? Please help
– Aditi
50 mins ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
3
down vote
accepted
There are $5^4$ roll sequences formed from the numbers 2, 3, 4, 5, 6 (and thus having minimum digit at least 2). Of these, $4^4$ roll sequences are formed from 3, 4, 5, 6, so cannot have minimum digit 2. The remaining $5^4-4^4$ sequences thus have minimum digit exactly 2, as required, and dividing by the $6^4$ rolls in total yields the correct probability.
answered 49 mins ago
Parcly Taxel
36.6k137095
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
1
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
add a comment |Â
up vote
3
down vote
Hint:
Your answer would be good if the question were "What is the probability that the minimum face is not $1$"?
answered 49 mins ago
ajotatxe
50.7k13185
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
Thank you for the hint !
– Aditi
42 mins ago
add a comment |Â
up vote
0
down vote
You can also calculate the numerator directly: 4*4^3 sequences have a single 2: 4C2*4^2 have two 2's; 4C3*4 sequences have 3 2's; 1 sequence of 2222 (all sequences containing no 1's). If you add these up, you get 369=5^4-4^4.
answered 29 mins ago
G. Thompson
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
There are $5^4$ roll sequences formed from the numbers 2, 3, 4, 5, 6 (and thus having minimum digit at least 2). Of these, $4^4$ roll sequences are formed from 3, 4, 5, 6, so cannot have minimum digit 2. The remaining $5^4-4^4$ sequences thus have minimum digit exactly 2, as required, and dividing by the $6^4$ rolls in total yields the correct probability.
answered 49 mins ago
Parcly Taxel
36.6k137095
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
1
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
add a comment |Â
up vote
3
down vote
accepted
There are $5^4$ roll sequences formed from the numbers 2, 3, 4, 5, 6 (and thus having minimum digit at least 2). Of these, $4^4$ roll sequences are formed from 3, 4, 5, 6, so cannot have minimum digit 2. The remaining $5^4-4^4$ sequences thus have minimum digit exactly 2, as required, and dividing by the $6^4$ rolls in total yields the correct probability.
answered 49 mins ago
Parcly Taxel
36.6k137095
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
1
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
add a comment |Â
up vote
3
down vote
accepted
up vote
3
down vote
accepted
There are $5^4$ roll sequences formed from the numbers 2, 3, 4, 5, 6 (and thus having minimum digit at least 2). Of these, $4^4$ roll sequences are formed from 3, 4, 5, 6, so cannot have minimum digit 2. The remaining $5^4-4^4$ sequences thus have minimum digit exactly 2, as required, and dividing by the $6^4$ rolls in total yields the correct probability.
answered 49 mins ago
Parcly Taxel
36.6k137095
There are $5^4$ roll sequences formed from the numbers 2, 3, 4, 5, 6 (and thus having minimum digit at least 2). Of these, $4^4$ roll sequences are formed from 3, 4, 5, 6, so cannot have minimum digit 2. The remaining $5^4-4^4$ sequences thus have minimum digit exactly 2, as required, and dividing by the $6^4$ rolls in total yields the correct probability.
answered 49 mins ago
Parcly Taxel
36.6k137095
answered 49 mins ago
Parcly Taxel
36.6k137095
answered 49 mins ago
Parcly Taxel
36.6k137095
answered 49 mins ago
Parcly Taxel
36.6k137095
36.6k137095
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
1
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
add a comment |Â
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
1
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
Ohhh I didn’t know that it was strict to have 2 in the answer . They never mentioned that $2$ must be one of the outcomes though so I was a bit confused. How do you deduce that $2$ must be one of the outcomes ?
– Aditi
47 mins ago
1
1
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
@Aditi The minimum face value is stipulated to be 2. This means that at least one die actually shows 2, to realise the minimum.
– Parcly Taxel
46 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
Ohh now I get it ! Thank you :)
– Aditi
45 mins ago
add a comment |Â
up vote
3
down vote
Hint:
Your answer would be good if the question were "What is the probability that the minimum face is not $1$"?
answered 49 mins ago
ajotatxe
50.7k13185
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
Thank you for the hint !
– Aditi
42 mins ago
add a comment |Â
up vote
3
down vote
Hint:
Your answer would be good if the question were "What is the probability that the minimum face is not $1$"?
answered 49 mins ago
ajotatxe
50.7k13185
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
Thank you for the hint !
– Aditi
42 mins ago
add a comment |Â
up vote
3
down vote
up vote
3
down vote
Hint:
Your answer would be good if the question were "What is the probability that the minimum face is not $1$"?
answered 49 mins ago
ajotatxe
50.7k13185
Hint:
Your answer would be good if the question were "What is the probability that the minimum face is not $1$"?
answered 49 mins ago
ajotatxe
50.7k13185
answered 49 mins ago
ajotatxe
50.7k13185
answered 49 mins ago
ajotatxe
50.7k13185
answered 49 mins ago
ajotatxe
50.7k13185
50.7k13185
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
Thank you for the hint !
– Aditi
42 mins ago
add a comment |Â
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
Thank you for the hint !
– Aditi
42 mins ago
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
Thank you , but how do we deduce that 2 must be one of the outcomes ?
– Aditi
46 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
You can't. Every roll could be fives and sixes (for example). There it is the point.
– ajotatxe
45 mins ago
Thank you for the hint !
– Aditi
42 mins ago
Thank you for the hint !
– Aditi
42 mins ago
add a comment |Â
up vote
0
down vote
You can also calculate the numerator directly: 4*4^3 sequences have a single 2: 4C2*4^2 have two 2's; 4C3*4 sequences have 3 2's; 1 sequence of 2222 (all sequences containing no 1's). If you add these up, you get 369=5^4-4^4.
answered 29 mins ago
G. Thompson
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
You can also calculate the numerator directly: 4*4^3 sequences have a single 2: 4C2*4^2 have two 2's; 4C3*4 sequences have 3 2's; 1 sequence of 2222 (all sequences containing no 1's). If you add these up, you get 369=5^4-4^4.
answered 29 mins ago
G. Thompson
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
You can also calculate the numerator directly: 4*4^3 sequences have a single 2: 4C2*4^2 have two 2's; 4C3*4 sequences have 3 2's; 1 sequence of 2222 (all sequences containing no 1's). If you add these up, you get 369=5^4-4^4.
answered 29 mins ago
G. Thompson
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
You can also calculate the numerator directly: 4*4^3 sequences have a single 2: 4C2*4^2 have two 2's; 4C3*4 sequences have 3 2's; 1 sequence of 2222 (all sequences containing no 1's). If you add these up, you get 369=5^4-4^4.
answered 29 mins ago
G. Thompson
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 29 mins ago
G. Thompson
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 29 mins ago
G. Thompson
11
answered 29 mins ago
G. Thompson
11
11
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
G. Thompson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
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$(5/6)^4$ is the probability that the minimum face value is $ge 2$.
– ncmathsadist
51 mins ago
@ncmathsadist so do you think that my answer is correct ? Please help
– Aditi
50 mins ago