Question

In a survey of U.S. adults with a sample size of 2062​,330said Franklin Roosevelt was the best president since World War II. TwoU.S. adults are selected at random from this sample without replacement.

​(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.
​(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.
​(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II.

Answer 1

Answer:

a) 0.0255

b) 0.7050

c) 0.2945

Step-by-step explanation:

Probability that one of those sampled saying that Roosevelt was the best president since World War II = 330/2062 = 0.16

Probability that one of those sampled don't mention Roosevelt = (2062 - 330)/2062 = 1732/2062 = 0.84

a) The probability that both adults picked say Franklin Roosevelt was the best president since World War II = (330/2062) × (329/2061) = 0.0255

b) The probability that neither of the two adults say Franklin Roosevelt was the best president since World War II = (1732/2062) × (1731/2061) = 0.7050

c) The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = Probability that one of the two adults mention Roosevelt + Probability that the two adults mention Roosevelt

Probability that one of the adults mention Roosevelt = [(330/2062) × (1732/2061)] + [(1732/2062) × (330/2061)] = 0.269

Probability that two of the adults mention Roosevelt has been done in (a) and it is equal to 0.0255

probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II = 0.269 + 0.0255 = 0.2945