Download 29) A basketball player is equally likely to make

3.4 29) A basketball player is equally likely to make and to miss his first shot of each game.
If he makes his first shot then he is twice as likely to make future shots as to miss them.
If he misses the first shot, then he is twice as likely to miss as to make future shots.
2/3 make
1/2 * 2/3 *2/3 = 2/9 2/3 make
1/3 miss
1/2 make
2/3 make
1/2 * 1/3 *2/3 = 1/9 1/3 miss
1/3 miss
Begin
1/3 make
1/2 * 1/3 *1/3 = 1/18 1/3 make
2/3 miss
1/2 miss
1/3 make
1/2 * 2/3 *1/3 = 1/9 2/3 miss
2/3 miss
a) In a game in which the player makes his third shot, find the probability that he
made his first shot as well.
Total =
2 1 1 1 1
   
9 9 18 9 2
Makes first shot:
2 1 1
 
9 9 3
Conditional probability =
1 1 1 2 2
   
3 2 3 1 3
b) In a game in which the player makes his third shot, find the probability that he
made all three shots.
Conditional probability =
2 1 2 2 4
   
9 2 9 1 9