In september 2008 the US Congress passed a financial bailout

In september 2008, the US Congress passed a financial bailout bill to help the economy. A survey conducted Swptember 19-22, 2008 asked Americans how this bailout bill made them feel. The results indicated that 56% of Republicans, 61% of Democrats, and 66% of Independents were angry. Suppose one adult is selected at random from each of these three political parties.

a) What is the probability that all three are angry?

b) What is the probability that all three are not angry?

c) What is the probability that exactly one of the three is angry?

d) What is the probability that at lease one is angry?

Solution

a) the probability that all three are angry = 0.56(0.61)(0.66) = 0.225456

b) the probability that all three are not angry = 0.44(0.39)(0.34) = 0.058344

c) the probability that exactly one of the three is angry = 0.56(0.39)(0.34) + 0.44(0.61)(0.34)+(0.44)(0.39)(0.66)

= 0.074256+0.091256+0.010296

= 0.175808

d) the probability that at lease one is angry= 1- all 3 are not angry = 1-0.058344 = 0.941656