Question

I don't know how to write (iii) and want to make sure my answer is right for (i) and (ii)

A prize competition operates by a machine choosing randomly (no replacement) 3 balls from 18. There are 6 red balls, 6 blue balls and 6 green balls. And for each colour the balls are numbered 1,2,3,4,5,6. There are three ways you can win: (C) you have three balls the same colour; (T) you have “top scores” meaning that the three numbers on your balls are all at least 4; (L) the “lucky ball” (the red ball with a ‘6’ on it) is one of your 3 balls.

(i) What are the probabilities of the three events C, L,T? Here and following, give exact answers as fractions and evaluate all binomial coefficients, etc. (You may find it best simply to compute how many of the 18 3 = 816 possibilities for the three balls satisfy each of the three conditions.)

(ii) What is the probability that you qualify for at least one of the three prizes?

(iii) The prize amounts are 3 units for (C), 2 units for (T) and 1 unit for (L). The rules state that if your balls qualify for multiple prizes, you receive only the largest of the prizes. What is the expected size of the prize you receive for one attempt at the competition?

Answer 1

i)Toal number of ways to choose 3 balls from a total of 18 balls is

Total number of ways event C can happen is 3balls are either blue or red or green = ways

Total number of ways event T can happen is

There is a total of 9 balls numbered 4,5,6

Total number of ways to select 3 balls from 9 is 84

if One of the ball is 6 of red than total number of ways to get 3 balls is

ii)

the probability that you qualify for at least one of the three prizes=0.3174

iii)

the expected size of the prize you receive for one attempt at the competition = expected size of the prize is 0.67