At a large block party, there are 40 men and 30 women. You want to ask opinions
ID: 3304464 • Letter: A
Question
At a large block party, there are 40 men and 30 women. You want to ask opinions about how to improve the next party. You choose at random four of the men and separately choose at random three of the women to interview. (Enter your answers to the nearest whole number.)
(a) What is the probability (in percent) that any of the 40 men is in your random sample of four men to be interviewed?___ %
B. What is the probability (in percent) that any of the 30 women is in your random sample of three women to be interviewed? ___ %
Explanation / Answer
No of ways of chosing r objects from n = nCr
a)
No of ways of chosing 4 men from 40 men = 40C4 = 91390
No of ways of in which on man is always selected among 4 selected men = 1* No of ways of chosing thee men from reamianing 39 men
= 1*(39C3) = 9139
probability (in percent) that any of the 40 men is in your random sample of four men to be interviewed = (9139/91390) = (1/10)*10 = 10%
b)
No of ways of chosing 3 women from 30 wonmen = 30C3 = 4060
No of ways of in which on woman is always selected among 3 selected women = 1* No of ways of chosing thee women from reamianing 29 women
= 1*(29C2) = 406
probability (in percent) that any of the 30 women is in your random sample of three women to be interviewed = (406/4060)*100 = (1/10)*100 = 10%
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