Question

Question Suppose that I know 20 jokes, of which 10 are funny ones. Suppose also that I am presenting a paper which will include 20 one-hour lectures, and that you turn up for every lecture. (i) If, before each lecture, I select a joke to tell uniformly at random from all the ones that I know and independently of any previous choices, what is the probability that you will hear every joke I know during the paper? What is the probability that you will hear at least one funny one? How many lectures would the paper have to include so that, on average, you would hear every joke that I know during the course of the paper? How many lectures would the paper have to include so that, on average, you would hear at least one funny joke in some lecture? (10 marks) Hint: The probability that you hear at least one funny joke is the same as 1 the probability that you hear NO funny ones. (ii) If before each lecture I select a joke independently at random from the ones that I know, such that I am twice as likely to select a funny one than an unfunny one, what is the proba bility that you will hear every joke I know? What is the probability that you hear at least one funny one? (10 marks)

kindly write properly so that i can understand the solution.

Answer 1

All possible case:

202 20

Case where you tell all the jokes: 20!

Hence, required probability is:

20!/2020 19!/201

P(atleast one funny)= 1-P(No funny joke)=

1 1020/20201- (0.5)2