You flip two coins and roll two sixsided dice What is the pr

You flip two coins and roll two six-sided dice. What is the probability that you get one head and one tail with the coins and two different numbers with the dice?

Solution

a)

There are 2*2 = 4 possibilities for the two coin tosses, and 2 ways so that we get a head and a tail.

Hence, P(HT, TH) = 2/4 = 1/2 = 0.5.

Also, there are 6*6 = 36 possibilities in the die rolls, and 6*5 = 30 ways so that we get two different numbers. Hence,

P(two numbers) = 30/36 = 5/6

Hence,

P(one H and one T and two distinct numbers) = (1/2)(5/6) = 5/12 [ANSWER]