Question

1.) Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities. (Enter the probabilities as fractions.)

(a) 5, given that the sum is odd

(b) odd, given that a 5 was rolled

2.) Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities. (Enter the probabilities as fractions.)

(a) 8, given that exactly one die came up 2.

(b) 6, given that exactly one die came up 2.

3.) Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities. (Enter the probabilities as fractions.)

(a) 6, given that a double was rolled

(b) a double, given that an 6 was rolled

Answer 1

1)

a) There are 36 possibilities. 18 of them are odd. Possible outcomes with a sum of 5 are: (1,4), (4,1), (2,3) and (3,2). The conitional probability is therefore 4/18 or 2/9.
b) If a sum of 5 is rolled, the sum is necessarily odd, so the conditional probability is 1.

2)

a) 1/5, there are 10 possibilities where there is a 2. Two of those ten add up to 8 . 2/10=1/5
(b) 1/5, same explanation as (a)

3)

1/5, when you roll a pair of dice, there are 36 possibilities total (6x6). Of those possibilities, only five of them add up to 6. Out of those 5, only one of them is a double