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Check it out! 1.5.2: The Binomial Distribution

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1 Check it out! 1.5.2: The Binomial Distribution
1.5.2: The Binomial Distribution

2 Carly bought 6 posters of different bands and hung them on the same wall of her bedroom. One poster in particular is her favorite. If Carly accidently knocks 1 random poster off the wall, what is the probability that the poster knocked down was her favorite? How many ways can Carly arrange all 6 posters in a straight line on the same wall? If Carly decides to move 2 of the posters to the opposite wall, how many different combinations of 2 posters can she possibly select? Common Core Georgia Performance Standards: MCC9–12.S.IC.4★ 1.5.2: The Binomial Distribution

3 If Carly accidently knocks 1 random poster off the wall, what is the probability that the poster knocked down was her favorite? In order to determine a probability, create a fraction in which the number of favorable outcomes is the numerator and the total possible outcomes is the denominator. 1.5.2: The Binomial Distribution

4 In this case, there is 1 favorite poster indicated out of 6 total posters.
Therefore, the probability that Carly knocked down her favorite poster is . 1.5.2: The Binomial Distribution

5 In this case, there are 6 items. Calculate 6!.
How many ways can Carly arrange all 6 posters in a straight line on the same wall? The number of ways to arrange all items in a group of n items is equal to n!. In this case, there are 6 items. Calculate 6!. 6! = 6 • 5 • 4 • 3 • 2 • 1 = 720 There are 720 ways for Carly to arrange the 6 posters in a straight line on the same wall. 1.5.2: The Binomial Distribution

6 items to choose from and r is the number of items actually chosen.
If Carly decides to move 2 of the posters to the opposite wall, how many different combinations of 2 posters can she possibly select? When asked to determine the number ways you can select 2 posters from the total of 6 posters, you are being asked to find a combination. For combinations, the order in which items are chosen does not impact the result. The general formula for calculating a combination is , where n is the total possible number of items to choose from and r is the number of items actually chosen. 1.5.2: The Binomial Distribution

7 In this scenario, n = 6 and r = 2.
Formula for calculating a combination Substitute 6 for n and for r. Simplify. Apply the factorial. 1.5.2: The Binomial Distribution

8 6C2 = 15 There are 15 ways Carly can choose 2 out of the 6 posters to put on the opposite wall. Connection to the Lesson Students will expand upon their understanding of probabilities and apply this concept to more sophisticated probability questions. 1.5.2: The Binomial Distribution


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