Suppose the player needs to make one of two free throws to win a game. The purple and red labels show P(2 hits) + P(1 hit) = 0.81 + 0.18 = 0.99.
The basketball player shoots 2 free throws—each independent of the other (pressure notwithstanding). The player will succeed on 0, 1, or 2 of them. You can compute the probabilities shown in the tree diagram by using the binomial probability formula.
Take Note Key Concept: Binomial Probability
Suppose you have n repeated independent trials, each with a probability of success p and a probability of failure q(with p + q = 1). Then the binomial probability of x successes in the n trials can be found by the following formula.
Problem 1 Using a Formula to Find Probabilities
Merchandising As part of a promotion, a store is giving away scratch-off cards. Each card has a 40% chance of awarding a prize. Suppose you have five cards. Find the probability that exactly four of the five cards will reveal a prize.
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Determine if this a binomial experiment.
- The situation involves 5 repeated trials—5 cards selected at random.
- Each trial has two possible outcomes: It is a winner or it is not.
- The probability of success is constant, 0.4, throughout the trials.
- The trials are independent. The outcome of scratching one card does not affect the probability of any of the other cards revealing a prize.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions