Thread: Probability Distributions

1. Suppose that one third of the cards in a scratch-and-win promotion gives a prize.

a) What is the probability that you will not win a prize until your second try?
b) What is the probability of winning within your first two tries?
c) What is the expected number of cards you would have to try before winning a prize?


I would really appreciate it if someone can help with this problem. it is due tomm so i really need to get it done. I have looked in the textbook and i have a feeling that it may have something to do with geometric distributions but i do not know what to do..

thanks

Originally Posted by Kiran

1. Suppose that one third of the cards in a scratch-and-win promotion gives a prize.

a) What is the probability that you will not win a prize until your second try?
b) What is the probability of winning within your first two tries?
c) What is the expected number of cards you would have to try before winning a prize?


I would really appreciate it if someone can help with this problem. it is due tomm so i really need to get it done. I have looked in the textbook and i have a feeling that it may have something to do with geometric distributions but i do not know what to do..

thanks

Let A be the event win a prize.

Pr(A) = 1/3
Pr(A') = 2/3

You must assume that there are a very large number of cards (why?).

I'll do (a) and (b) from first principles:

(a) The favourable sequence of events is A' A so you want Pr(A',A) = (2/3)(1/3) = 2/9.

(b) The favourable sequence of events is A or A' A so you want Pr(A or A',A) = 1/3 + 2/9 = 5/9.

(c) Basic formula: Mean = 1/p = 1/(1/3) = 3.

No offence chum but the questions you're posting are very routine and strongly indicate that you need to thoroughly revise this area of study, paying particular attention to worked examples. In particular, (c) requires only the simplest application of the basic formula ....