Question

We roll two fair 6-sided dice, A and B. Each one of the 36 possible outcomes is assumed to be equally likely.

a. Find the probability that dice A is larger than dice B.

b. Given that the roll resulted in a sum of 5 or less, find the conditional probability that the two dice were equal.

c. Given that the two dice land on different numbers, find the conditional probability that the two dice differed by 2.

Answer 1

a)there are 30 ways in which outcomes are unuequal , and out of this 30, exactly half 15 are when A is greater than B and in 15 B is greater than A

P( dice A is larger than dice B ) =15/36 =5/12

b)

number of ways sum is 5 or less =N(sum is 2)+N(sum is 3)+N(sum is 4)+N(sum is 5)=1+2+3+4=10

number of ways sum is 5 or less and both dice are equal =2 (which are (1,1),(2,2))

therefore conditional probability that the two dice were equal given sum is 5 or less =2/5

c)

number of ways two dice are different =30

number of ways dice are different and dice differed by 2 =8

therefore probability =8/30 =4/15