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)
- Find the probability that the first free throw shot Dwight makes is the fourth shot. Is this an unusual event? Explain.
- 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 $q=1- p=1-0.602 = 0.398$.
- 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.
- 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.
Further Reading
- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators
