1. (4) Suppose you roll a dice twice. Calculate the probability of the following

Question

1. (4) Suppose you roll a dice twice. Calculate the probability of the following (a) the sum of the dice rolls is 3 or 7. (b) the sum of the dice is greater than 7 and is an odd number. 2. (4) A classroom consists of 30 students. 12 students are male. 14 students have blonde hair. The number of blonde males in the classroom is 8. (a) What is the probability a randomly selected student is female with non-blonde hair? (b) What is the probability a student is female given he/she has blonde hair? 3· (2) A bag contains 20 balls, 13 are green and 7 are red. You want to draw two balls from the bag (a) What is the probability the first ball is green AND the second ball is green? (b) You draw one ball, find it is green, and put it aside. What is the probability that the second drawn ball is red?

Explanation / Answer

1) a) P = P(sum is 3) + P(sum is 7)

Total outcomes = 36 as (1,1), (1,2) and so on till (6,6)

P = 2/36 +6/36

P = 0.22

b) P = greater than 7 and odd number can be 9 or 11

The sum of 9 can be rolled in 4 ways:

A={(3,6),(4,5),(5,4),(6,3)}

There are two ways to roll an 11: (5,6),(6,5)

So, P = 4/36 + 2/36

P = 0.167

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