Question

1. Suppose that a friend gives us the chance to participate in a game. The game is as follows. There is a bucket containing 6 green tokens and 18 red tokens. We are to blindly reach into the bucket and randomly choose one token. Keeping this token (i.e. the chosen token is not returned to the bucket) we are to once again reach in blindly and randomly retrieve another token. If the first token we have chosen is green and the second is red then we win the game. Otherwise we lose. Define the two events below as follows: Gi-first token selected is green. R2 second token selected is red 3 marks) (a) What is P(Gı)? 4 marks) b) In words, explain what the event R2|Gı is 4 marks) (c) What is P(R2 Gi)? 4 marks) (d) What is P(Gı and R2)?

Answer 1

a) There are a total of 6 green +18 red = 24 tokens

P(G₁) = P(First Token selected is green) = Selecting 1 green token from 6 green / Selecting 1 token from 24 token

(16 1 24 4

b) R₂|G₁ = 2nd draw results in  a red token drawn, given that the first draw resulted in a green token

If the first draw results in a green token and we do not return it to the bucket , then at the time of second draw we will be dealing with 5 green + 18 red = 23 tokens

c) P(R₂|G₁ )= Selecting 1 red token from 18 green / Selecting 1 token from 23 token

18 23 23

d)

끓·| = 18 9 23 4 46 PlG, and Ra) = P(RIG, )P(G, ) =