Binomial Distribution Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
A basketball player has a 70%70\% free-throw success rate. In 66 attempts, what is the probability of making exactly 44?

Solution

  1. 1
    (64)=15\binom{6}{4} = 15, p=0.7p = 0.7, 1−p=0.31 - p = 0.3.
  2. 2
    P(X=4)=15×(0.7)4×(0.3)2=15×0.2401×0.09=15×0.021609≈0.324P(X = 4) = 15 \times (0.7)^4 \times (0.3)^2 = 15 \times 0.2401 \times 0.09 = 15 \times 0.021609 \approx 0.324.

Answer

P(X=4)≈0.324P(X = 4) \approx 0.324
The binomial model applies because each free throw is independent with a constant probability of success.

About Binomial Distribution

The probability distribution of the number of successes in nn independent yes/no trials, each with probability pp.

Learn more about Binomial Distribution →

More Binomial Distribution Examples

Example 1 medium

A fair coin is flipped [formula] times. What is the probability of getting exactly [formula] heads?

Example 2 hard

A multiple-choice quiz has [formula] questions, each with [formula] choices. If a student guesses ra

Example 4 medium

A student guesses on [formula] true-or-false questions. What is the probability of getting at least

← All Binomial Distribution Examples Binomial Distribution Concept