Mathematics 30 Online
OpenStudy (anonymous):

A pair of fair dice is tossed 3 times. Find the probability a seven appears 3 times.

OpenStudy (anonymous):

i'm gonna go with 16.67%^3=0.00463241...

OpenStudy (anonymous):

probability that seven appears on one throw = 6/36 = 1/6 probability that it appears 3 times = 1/6 *1/6*1/6 = 1/216

OpenStudy (anonymous):

So, as a percentage, 0.463%

OpenStudy (anonymous):

thats correct but what happens when if they ask you to Find the probability a 7 or 11 appears at least twice.

OpenStudy (anonymous):

it is a binomial probability... probability that 7 or 11 appear on one throw = 8/36 = 2/9 probability that 7or 11 appear at least 2 times = 3C2 * (2/9)^2 * (7/9)

OpenStudy (anonymous):

P(7) =0 unless you're looking at the probability that the sum is 7...but a fair die has numbers 1 to 6 only...no 7...thus P(7) = 0 for each toss...and thus 0 overall...

OpenStudy (anonymous):

GODinme it is the sum of 7 or 11

OpenStudy (anonymous):

sorry, it is probability that 7 or 11 appear exactly 2 times. for at least 2 times please add this also... 3C3 *(2/9)^3

OpenStudy (anonymous):

ok...that wasn't in the question...who's asking the question?

OpenStudy (anonymous):

7 or 11? Thats a Craps problem...Google will help...

OpenStudy (anonymous):

OpenStudy (anonymous):

so how do you know what it's sposed to be?

OpenStudy (anonymous):

it was a two part question you know it is a sum because of course there isnt a 7 or a 11. The question was a two parts. I got the first answer from the first two replies. the second part is "A pair of fair dice is tossed 3 times.Find the probability a 7 or 11 appears at least twice.

OpenStudy (anonymous):

probability that 7or 11 appear at at least 2 times = 3C2 * (2/9)^2 * (7/9) + 3C3 *(2/9)^3

OpenStudy (anonymous):

probability of a 7, 1/6th probability of an 11, 1/18th. Multiply ad nauseum...

OpenStudy (anonymous):

ok...then it can be represented as a binomial distribution: n=3, P(7) = 1/6 for any throw...and each throw is independent... thus: 3C3*(1/6)^3*(5/6)^0 + 3C2*(1/6)^2*(5/6)^1 P(11) = 1/18 so similarly: 3C3*(1/12)^3 + 3C2*(1/12)^2*(11/12)^1 the sum ofr P(7) + P(11) is what is wanted...

OpenStudy (anonymous):

sorry, your solution is wrong... probability that 7 or 11 appear on one throw of a pair of dice = 1/6 + 2/36 = 8/36 = 2/9 P(AUB) = P(A) + P(B) here P(A n B) = 0

OpenStudy (anonymous):

i think you're right...i approached it from a different angle but i think i messed it up that way...thanks...

OpenStudy (anonymous):

ok....