1. Answer the following questions. You don\'t need to show your work. Questions
ID: 3063525 • Letter: 1
Question
1. Answer the following questions. You don't need to show your work. Questions a-d are based on the following scenario: Production line l of a factory works 60% of the time, while production line 11 works 70% of the time, independently of each other. Questions e-i are based on the following scenario. Suppose that each child born to a couple is equally likely to be a boy or a girl independent of the sex distribution of the other children of the family. Suppose the couple has 5 children a. What is the probability that both lines operate? b. What is the probability that both lines are stopped? c. What is the probability that at least one of the lines operate? d. What is the probability that precisely one of the lines operate? e. What is the probability that all children are of the same sex? f. What is the probability that the 3 eldest are boys and the others are girls? g. What is the probability that exactly 3 are boys? h. What is the probability that the 2 oldest are girls? i. What is the probability that there is at least 1 girl?Explanation / Answer
Given that
probability of line I works = 0.6
Probabilty of line II works = 0.7
a) probability of both the lines = 0.6*0.7 = 0.42
b) probability of both are stopped = 1 - 0.42 = 0.58
c) probability of atleast one line works = 0.6 + 0.7 - 0.42 = 0.88
d) probability of one of the line works = 0.6 * 0.3 + 0.7*0.4 = 0.46
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