A fair coin is flipped seven times. What is the probability that heads occurs exactly 6 times if it is known that heads occurs at least four times? Two machines turn out all the products in a factory, with the first machine producing 35% of the product and the second 65%. The first machine produces defective products 7% of the time and the second machine 9% of the time. (a) What is the probability that a defective part is produced at this factory given that it was made on the first machine? (b) What is the probability that a defective part is produced at this factory? A door-to-door salesman expects to make a sale 22% of the time when starting the day. But making a sale increases his enthusiasm so much that the probability of a sale to the next customer is 0.48. If he makes no sale, the probability for a sale to the next customer stays at 0.22. What is the probability that he will make at least two sales with his first three visits?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A fair coin is flipped seven times. What is the probability that heads occurs exactly 6 times if
it is known that heads occurs at least four times?
Two machines turn out all the products in a factory, with the first machine producing 35%
of the product and the second 65%. The first machine produces defective products 7% of
the time and the second machine 9% of the time.
(a) What is the probability that a defective part is produced at this factory given
that it was made on the first machine?
(b) What is the probability that a defective part is produced at this factory?
A door-to-door salesman expects to make a sale 22% of the time when starting the day.
But making a sale increases his enthusiasm so much that the probability of a sale to the
next customer is 0.48. If he makes no sale, the probability for a sale to the next customer
stays at 0.22. What is the probability that he will make at least two sales with his first three
visits?
Transcribed Image Text:A fair coin is flipped seven times. What is the probability that heads occurs exactly 6 times if it is known that heads occurs at least four times? Two machines turn out all the products in a factory, with the first machine producing 35% of the product and the second 65%. The first machine produces defective products 7% of the time and the second machine 9% of the time. (a) What is the probability that a defective part is produced at this factory given that it was made on the first machine? (b) What is the probability that a defective part is produced at this factory? A door-to-door salesman expects to make a sale 22% of the time when starting the day. But making a sale increases his enthusiasm so much that the probability of a sale to the next customer is 0.48. If he makes no sale, the probability for a sale to the next customer stays at 0.22. What is the probability that he will make at least two sales with his first three visits?
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