Assume that the probability that an individual changes residence during the year
ID: 3060376 • Letter: A
Question
Assume that the probability that an individual changes residence during the year is 0.21. A survey is taken of five individuals. (a) Write out the elements in the sample space. (b) What is the probability that exactly three out of the five individuals move during the year? (c) What is the probability that at least one of the five individuals moves during the year? Assume that the probability that an individual changes residence during the year is 0.21. A survey is taken of five individuals. (a) Write out the elements in the sample space. (b) What is the probability that exactly three out of the five individuals move during the year? (c) What is the probability that at least one of the five individuals moves during the year? Assume that the probability that an individual changes residence during the year is 0.21. A survey is taken of five individuals. (a) Write out the elements in the sample space. (b) What is the probability that exactly three out of the five individuals move during the year? (c) What is the probability that at least one of the five individuals moves during the year?Explanation / Answer
(a) Let "c" denote an individual changing residence and "nc" denote an individual not changing residence. Hence, the sample space is given below for all the five individuals.
(b) Let A be an event denoting exactly 3 out of 5 individuals moving during the year. Out of the 32 cases listed above, there are 10 cases favourable to event A.
Therefore, probability = 10/32 = 0.3125
(c) Let B be an event denoting at least 1 out of 5 individuals moving during the year. Out of the 32 cases listed above, there are 31 cases favourable to event B.
Therefore, probability = 31/32 = 0.9688
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