Question

A basketball player is shooting free throws blindfolded. He shoots in groups of 4 shots. Assume that it is equally likely that he will hit or miss a shot. Design and do a simulation to determine the probability that he will hit at least 75% of his shots within the groups. (Hint: Use coins.)

Answer 1

Use 4 coins. Let heads = hit and tails = miss. Toss each coin and record the results in a table. Coin 1Coin 2Coin3Coin 4Set 1HHHHSet 2HTHHSet 3HHTHSet 4THTTSet 5

Repeat the coin tosses until you have recorded 50 sets of 4 tosses each. b. Count the successful outcomes—those with three or four heads. Coin 1Coin 2Coin3Coin 4SuccessSet 1HHHHxSet 2HTHHxSet 3HHTHxSet 4THTTSet 5

Explanation:

Answer 2

Let H represent hit and M represent miss, Then sample space

MMMM, MMMH, MMHM, MHMM, HMMM, MMHH, MHMH, HMMH, MHHM, HMHM, HHMM, MHHH, HMHH, HHMH, HHHM, HHHH

He hit at least 75% in 5 occasions.

Therefore, P(hit at least 75%) = 5/16