A bag has 5 white & 3 red balls. 2 players, A&B, take turns @drawing 1 ball frm the bag @ random, & balls aren't replacd. 'A' draws 1st,Find P(A is the winner /the winning player wins on his 2nd draw)

Question

The player who first gets two red balls is the winner, and the drawing stops as soon as either player has drawn two red ball

Answer 1

If the winner wins on his second draw then 3 balls have been drawn, 2 by player A and one by player B.

A draws. P(RED) on first draw is 3/8, P(WHITE)=5/8. After A has drawn a red, there are 7 balls left, 5W+2R. B draws: P(RED)=2/7, P(WHITE)=5/7. Now A draws again. There are only 6 balls left, and if B has drawn red, then there is only one red left, so P(RED)=1/6; if B drew white, there are still two reds left, so P(RED)=2/6. So the results of drawing resulting in A as the winner are RWR (3/8*5/7*2/6=5/56) or RRR (3/8*2/7*1/6=1/56). Either possibility makes A the winner so P=5/56+1/56=6/56=3/28.