4.1 Suppose that 31% of Democrats and 63% of Republicans support building more n

Question

4.1 Suppose that 31% of Democrats and 63% of Republicans support building more nuclear power plants in the United States. Now suppose that there are 40 Republicans and 35 Democrats in one room

.a. What is the probability of randomly selecting a Republican from this room?

b. What is the probability of randomly selecting a Democrat from this room?

c. What is the probability of randomly selecting a Republican who supports building more nuclear power plants?

d. What is the probability of randomly selecting a Democrat who supports building more nuclear power plants?

e. What is the probability of randomly selecting one Democrat and one Republican who both support building more nuclear power plants?

f. What is the probability of randomly selecting two Republicans who do not support building more nuclear power plants?

Explanation / Answer

a. probability of randomly selecting a Republican = 40 / (40+35) = 40/75 = 0.5333

b. probability of randomly selecting a Democrat = 35/75 = 0.4667

c. probability of randomly selecting a Republican who supports building more nuclear power plants = 40* 63% / 75

= 0.336

d. probability of randomly selecting a Democrat who supports building more nuclear power plants = 35 * 31% / 75

= 0.1447

e. the probability of randomly selecting one Democrat and one Republican who both support building more nuclear power plants = (40 * 63%) * (35 * 31%) / 75C2 = 0.0985

f. the probability of randomly selecting two Republicans who do not support building more nuclear power plants

= (40*(100-63)% / 75)2 = 0.0389

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