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