In a survey of 1010 married adults, the participants were asked the question: Wa

Question

In a survey of 1010 married adults, the participants were asked the question: Was a good credit score important when choosing your spouse? Four hundred and ninety-five answered in the affirmative, while 515 answered in the negative. If 8 of those surveyed were selected at random, what is the probability of the following?† (Round your answers to four decimal places.)

(a)

None answered in the affirmative?

(b)

Exactly 6 answered in the affirmative?

(c)

More than 6 answered in the affirmative?

(d)

At least 1 answered in the affirmative?

Explanation / Answer

P(affirmative) = 495/1010 = 0.49

P(negative) = 515/1010 = 0.51

8 out of those surveyed are selected at random

(a) P(none of them are affirmative) = 8C0*(0.49)0*(0.51)8 = 0.0046

(b) P(6 as affirmative) = 8C6*(0.49)6*(0.51)2 = 0.1008

(c) P(>6 as affirmative) = 8C6*(0.49)6*(0.51)2 + 8C7*(0.49)7*(0.51)1 + 8C8*(0.49)8*(0.51)0 = 0.1318

(d) P(atleast 1 affirmative) = 1-P(none affirmative) = 1-P(0 affirmative) = 1-0.0046 = 0.9954

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