Question

(c) If you buy 4 spark plugs, what is the probability that at least one is defective? 5. At Least One Girl: Suppose a couple plans to have 4 children and the probability of a boy is 0.50. Find the probability that the couple has at least one girl. 6.* Lie Detector: Suppose a lie detector test can detect a lie 95% of the time. You get hooked up and tell 10 truths and 10 lies. What is the probability that at least one of your lies goes undetected? 7. Alarm Clock - Redundancy: You have two alarm clocks. The first one is successful 95% of the time and the second one is successful 60% of the time it turns out your second one was actually less reliable than the first). (a) Suppose you only remember to set the good alarm clock. What is the probability that it will succeed on the morning of an important exam? (b) Suppose you set both alarm clocks. What is the probability that at least one of them is successful on the morning of an important exam? (c) This practice of using a second device is called redundancy. Was there a significant increase in the probability of getting to the exam obtained using the second alarm clock?

Answer 1

Please let me know in case you've question on the answer. Answering 5 , as we are allowed to answer 1 question per post.

5.

There are 4 children.

Given: p(boy) = .50

P(atleast one girl)

= 1- P(none is a girl out of the 4) [this is called solving by complementry method]

= 1- 4C4*.5^4*.5^0

= 1- 1*.0625

= .9375

Answer: Probability that couple has at least 1 girl = 0.9375