Question

A basketball player takes 20 shots per game. The odds of making any single shot are 1 to 3. All shot attempts are independent, i.e. there are no “hot streaks". What is the probability that the player will make 5 or more shots in a game? Hint: First find the probability of making a single shot. Define a random variable X to represent the number of shots made in a game. State a reasonable probability distribution for X. Finally, you want to know P(X => 5).

Answer 1

The odds of making any single shot are 1 to 3. Therefore the probability of making a shot is computed here as: 1/(1 + 3) = 1/4 = 0.25

The number of shots out of the 20 shots taken could be modelled here as:

The probability now is computed using the binomial probability function as:

Therefore 0.5852 is the required probability here.