Solve a and b When we analyzed our algorithm for generating random primes, we us

Question

Solve a and b

When we analyzed our algorithm for generating random primes, we used the following useful fact: Suppose each time you pull the arm of a slot machine, you have a probability p of winning. Then the expected number of times you have to pull the arm in order to win is 1/p. Using this fact, answer the following questions. What is the expected number of times you need to roll a die in order to get a six? A pond contains 20 catfish and 980 eels. You repeatedly pull a random fish out of the pond and then throw it back in. What is the expected number of times you need to do this until you get a catfish?

Explanation / Answer

1.

Total number of outcomes of a dice throwing is = 6 {1,2,3,4,5,6}

probability of getting a 6 in a throw = no.of times 6 can appear in a through/total possible outcomes = 1/6

So, by given formulae above to get a 6 in a dice through you need to roll a dice = 1/probability of getting a 6 , number of times

so the expected number of times you need to roll a die in order to get a six = 1/ (1/6) = 6 number of times

2 .

total number of outcomes possible = 1000 {20catfish + 980 eels}

total number of possible outcomes for drawn fish to be catfish = 20

so probability of a fish being drawn is a cat fish is = total number of favoured outcomes / total number of possible outcomes = 20/1000

and for a drawn fish to be a catfish expected number of times you need to draw is given by above formulae = 1/ probability of fish dran being a cat fish = 1 / (20/1000) = 1000/20 = 50

so you need to draw 50 number of times on an average to get a fish of catfish type in a random event .

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