The probability that a marriage will end in divorce within 2

The probability that a marriage will end in divorce within 20 years after its start is 0.84. Six couples are chosen at random to participate in this study.

What is the probability that, in the next 20 years all will be divorced?
A. 1.0000 B. 0.3513 C. 0.0005 D. 0.00002

8. Give the average number of couple that will be divorced in the next 20 years. Round to the nearest whole number.
A. 3 B. 6 C. 2 D. 5 E. 1

Solution

probability that a marriage will end in divorce within 20 years after its start is 0.84

(a) probability that, in the next 20 years all will be divorced = 0.84 x 0.84 x 0.84 x 0.84 x 0.84 x 0.84 = 0.3513

Hence option (B)

(b) average number of couple that will be divorced in the next 20 years = 6 x 0.84 = 5.04 = 5 (nearest whole no)

Hence option (D)

Note : average number of couple that will be divorced in the next 20 years id calculated using binomial probability distribution . where mean = np

n = no. of trials (here 6 couples)

p = the probability of success in a single trial (0.84 here)