Toy Surprise INSIDE Cracker Jack NET WT. 4h 02, (127.5p Suppose a box of Cracker

Question

Toy Surprise INSIDE Cracker Jack NET WT. 4h 02, (127.5p Suppose a box of Cracker Jacks contains one of 5 toy prizes: a small rubber ball,a whistle, a Captain America decoder ring, a race car, or a magnifying glass. Each prize is equally likely to be in a box. Question 1. How many boxes of Cracker Jacks would you expect to buy until you obtain a complete set of prizes? Many human skin tumors contain mutated p53 genes that probably result from excess UV exposure. One of 10 different equally likely mutations of the p53 gene always results from a single episode of excessive UV exposure; the 10 mutations remain equally likely over repeated exposures. A p53 gene must experience all 10 mutations before a tumor can develop. Assume that only one mutation can occur as a result of one excessive UV skin exposure. Question 2. How many excessive UV exposures would you expect are required until the p53 gene has experienced all 10 mutations? ue.efureof

Explanation / Answer

Ans-1. By using geometric rv.

The first box you buy necessarily gives you a prize you don't yet have. After you have the first prize, when you buy another box the probability is p=4/5=0.8 that you get a different prize,

So the expected number of boxes until you get a different prize is 1/0.8=10/8

After you have 2 prizes, when you buy another box the probability is 3/5 that you get a different prize

so the expected number of boxes until you get a different prize is 10/6 And so on.

After you have 4 prizes, when you buy another box the probability is 1/5 that you get a different prize, so the expected number of boxes until you get a different prize is 10/2=5

So the expected number of boxes needed to get all 5 prizes is 1+10/8+10/6+10/4+10/2=11.42

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