In: Statistics and Probability
Auto Repair Insurance. A person calls people to ask if they would like to extend their automobile insurance beyond the normal 3 years. The probability that the respondent says yes is about 33%. If she calls 12 people, find the probability that the first person to say yes will occur with the fourth customer.
p = 0.33
4th customer is the 1st one to yes. So, first 3 no and then yes
q = 1 - 0.33 = 0.67
P(4th is 1st one to say yes) = 0.67*0.67*0.67*0.33 = 0.09925179
In general we need to round off to 4 decimal places hence 0.0993 or 0.09925179 is the answer.
Please comment if any doubt.