Kindergarten class has 7 Scooby Doo , 8 Sesame Street, and 9 Barney DVDs. Each week, the class randomly selects 2 DVDs to watch on Friday. What is the probability that both movies are Barney?
there are 24C2 ways of selecting two movies
there are 9C2 ways of selecting two Barney movies
the probability is ... 9C2 / 24C2
To find the probability that both movies are Barney, we first need to determine the total number of possible outcomes. Each week, the class randomly selects 2 DVDs out of a total of 7 Scooby Doo, 8 Sesame Street, and 9 Barney DVDs.
The total number of possible outcomes can be calculated using combinations. The formula for combinations is:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items and r is the number of items selected.
In this case, we need to calculate C(24, 2) since there are 7 Scooby Doo, 8 Sesame Street, and 9 Barney DVDs.
C(24, 2) = 24! / (2! * (24 - 2)!)
= 24! / (2! * 22!)
= (24 * 23 * 22!) / (2! * 22!)
= (24 * 23) / 2
= 276
Therefore, there are 276 possible outcomes.
Next, we need to determine the number of favorable outcomes, i.e., the number of outcomes where both movies are Barney. Since there are 9 Barney DVDs, the number of favorable outcomes is given by C(9, 2):
C(9, 2) = 9! / (2! * (9 - 2)!)
= 9! / (2! * 7!)
= (9 * 8) / (2 * 1)
= 36
Therefore, there are 36 favorable outcomes.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
= 36 / 276
≈ 0.13 or 13%
So, the probability that both movies selected are Barney is approximately 0.13 or 13%.