Binomial probability - Math Central

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Question from Rana:

According to one study, it has been claimed that 65% of all single men in Montreal would welcome a
woman taking the initiative in asking for a date. You decide to challenge this study by performing a little experiment of your own. You randomly select 15 single men from around Montreal and ask them if they would be comfortable with a woman asking them out for a date. If the claim made by the study was true, what is the probability that:
a) Exactly 9 men would say yes?
b) Exactly 6 men would say no?
c) More than 11 men would say yes?
d) At most 4 men would say no?

Hi Rana,

I can get you started by showing you how to solve part a).

If the probability that a single male would welcome a woman taking the initiative in asking for a date is 0.65 and you randomly and independently select 15 single men and ask them if they would welcome a
woman taking the initiative in asking for a date then you are working with a binomial distribution. The sample size is n = 15 and the probability of success (a man answering yes to your question) is 0.65. The binomial distribution then says that the probability of r successes is

For part a) you have r = 9 and hence the probability that exactly 9 men say yes is

Penny

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