# Solved: In Exercises 5 and 6, use the following information. Basketball player Dwight Howard makes a free th

#### ByDr. Raju Chaudhari

Oct 15, 2020

In Exercises 5 and 6, use the following information. Basketball player Dwight Howard makes a free throw shot about 60.2% of the time. (Source: ESPN)

1. Find the probability that the first free throw shot Dwight makes is the fourth shot. Is this an unusual event? Explain.
2. Find the probability that the first free throw shot Dwight makes is the second or third shot. Is this an unusual event? Explain.

#### Solution

The probability of making a free shot is $p=0.602$, so the probability of not making a free shot is $q=1- p=1-0.602 = 0.398$.

1. The probability that the first free throw shot Dwight makes is the fourth shot is

 \begin{aligned} q*q*q*(1-p) &= 0.398*0.398*0.398*0.602\\ &= 0.038 \end{aligned}
The probability is about 4%, which is quite low. So it is an unusual event.

1. The probability that the first free throw shot Dwight makes is the second or third shot is

 \begin{aligned} (q*p) + (q*q*p) &=(0.398*.602) + (0.398*0.398*0.602)\\ & =0.335 \end{aligned}

The probability is about 33%, which is not low. So it is not an unusual event.