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 6 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?

Answer 1

The answer is 0.0173

Explanation:

The probability that none of the surveyed answered in the affirmative is the probability that all of the surveyed answered negative.

The probability of one person picked and answered negative is
`(515)/(1010)`

The probability of second person picked and answered negative is
`(514)/(1009)`

The probability of third person picked and answered negative is
`(513)/(1008)`

Going like this:

The probability of sixth person picked and answered negative is
`(510)/(1005)`

Thus

P(all negative) =
`(515*514*513*512*511*510)/(1010*1009*1008*1007*1006*1005)` =0,0173

This formula can also expressed as

Combination of 6 from 512 ÷ Combination of 6 from 1010