Need help answering this question 3.8.7 You walk into your favorite arcade and d

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Need help answering this question

3.8.7 You walk into your favorite arcade and decide that you are going to play one of the eight claw games that are lined up against one wall. In each machine, there is a claw that you need to move so that when the claw is released, it reaches down and picks up a toy. Each time you play, you get to release the claw three times. Each machine contains 10 toys and in each machine, eight of the toys are secretly marked with free passes to Wild Water Kingdom. a) You walk up to the first machine. What is the probability you can get three winning toys playing the game only once. Assume that you cannot pick up more than one toy at a time and that you are so good at the game that you get a toy every time the claw is released. b) Assume there are 8 machines with the same setup as the first machine. You manage to get the three winning toys in exactly 5 out of 8 machines. The other three machines you don't get any. What is the probability of that happening?

Explanation / Answer

Here, probability of winning toys = 8/10 = 0.8

(a) P(3 winning toys from first machine playing once) : (0.8)(0.8)(0.8) = 0.512

(b) now p = 0.512 and n = 8

Let x be the number of machines with 3 winning toys

P(x=5) : 8C5 (0.512)5 (1-0.512)8-5 = 0.2290

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