SOLUTION: A game consists of throwing tennis ball into a bucket from a given distance. The probability that Bob will get the tennis ball in the bucket is 0.4 . A turn consists of three attem

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Question 1203301: A game consists of throwing tennis ball into a bucket from a given distance. The probability that Bob will get the tennis ball in the bucket is 0.4 . A turn consists of three attempts. Construct a PDT of X, the number of tennis balls that land in the bucket in a turn.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


This is a good exercise in basic binomial probability. Calculate the probabilities of 0, 1, 2, or 3 balls in the bucket and verify that the sum of the probabilities is 1.

If Y (yes) represents a ball in the bucket and N (no) represents a ball not in the bucket, then the probability distribution for the game is found using

%280.4Y%2B0.6N%29%5E3

0 balls....

C%283%2C0%29%28%280.4%29%5E0%29%28%280.6%29%5E3%29=%281%29%281%29%280.216%29=0.216

1 ball....

C%283%2C1%29%28%280.4%29%5E1%29%28%280.6%29%5E2%29=%283%29%280.4%29%280.36%29=0.432

2 balls....

C%283%2C2%29%28%280.4%29%5E2%29%28%280.6%29%5E1%29=%283%29%280.16%29%280.6%29=0.288

3 balls....

C%283%2C3%29%28%280.4%29%5E3%29%28%280.6%29%5E0%29=%281%29%280.064%29%281%29=0.064

The PDT for the game....
 balls probability
   0    0.216
   1    0.432
   2    0.288
   3    0.064

CHECK: 0.216 + 0.432 + 0.288 + 0.064 = 1.000