1 / 8

Essential Questions

Essential Questions. How do we use the Binomial Theorem to expand a binomial raised to a power? How do we find binomial probabilities and test hypotheses?.

singere
Télécharger la présentation

Essential Questions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Essential Questions • How do we use the Binomial Theorem to expand a binomial raised to a power? • How do we find binomial probabilities and test hypotheses?

  2. A binomial experimentconsists of n independent trials whose outcomes are either successes or failures; the probability of success p is the same for each trial, and the probability of failure q is the same for each trial. Because there are only two outcomes, p + q = 1, or q = 1 -p. Below are some examples of binomial experiments:

  3. Suppose the probability of being left-handed is 0.1 and you want to find the probability that 2 out of 3 people will be left-handed. There are 3C2 ways to choose the two left-handed people: LLR, LRL, and RLL. The probability of each of these occurring is 0.1(0.1)(0.9). This leads to the following formula.

  4. The probability that Jean will make each free throw is , or 0.5. Example 1: Finding Binomial Probabilities Jean usually makes half of her free throws in basketball practice. Today, she tries 3 free throws. What is the probability that Jean will make exactly 1 of her free throws? P(r) = nCr prqn-r Substitute 3 for n, 1 for r, 0.5 for p, and 0.5 for q. P(1) = 3C1 (0.5)1 (0.5)3-1 The probability that Jean will make exactly one free throw is 37.5%.

  5. Example 2: Finding Binomial Probabilities Jean usually makes half of her free throws in basketball practice. Today, she tries 3 free throws.What is the probability that she will make at least 1 free throw? At least 1 free throw made is the same as exactly 1, 2, or 3 free throws made. P(1) + P(2) + P(3) + 3C2(0.5)2(0.5)3-2 + 3C3(0.5)3(0.5)3-3 3C1(0.5)1(0.5)3-1 The probability that Jean will make at least one free throw is 87.5%.

  6. The probability that the counselor will be assigned 1 of the 3 students is . Substitute 3 for n, 2 for r, for p, and for q. Example 3: Finding Binomial Probabilities Students are assigned randomly to 1 of 3 guidance counselors. What is the probability that Counselor Jenkins will get 2 of the next 3 students assigned? The probability that Counselor Jenkins will get 2 of the next 3 students assigned is about 22%.

  7. Example 4: Finding Binomial Probabilities Ellen takes a multiple-choice quiz that has 5 questions, with 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing? At least 2 answers correct is the same as exactly 2, 3, 4, or 5 questions correct. The probability of answering a question correctly is 0.25. P(2) + P(3) + P(4) + P(5) 5C2(0.25)2(0.75)5-2 + 5C4(0.25)4(0.75)5-4 + 5C3(0.25)3(0.75)5-3 + 5C5(0.25)5(0.75)5-5

  8. Lesson 3.3 Practice B

More Related