there are 3 miniature chocolate bars and 5 peaunt butter cups in a candy dish. judie chooses 2 of them at random. What is the probablity that both she chooses 2 miniature choclate bars?
To find the probability of Judie choosing 2 miniature chocolate bars, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Judie is choosing 2 candies out of a total of 8 candies (3 miniature chocolate bars + 5 peanut butter cups). We can use the combination formula, nCr, to calculate the number of ways to choose 2 candies out of 8 candies:
Total possible outcomes = 8C2 = 8! / (2! * (8-2)!)
= 8! / (2! * 6!)
= (8 * 7) / (2 * 1)
= 28
Number of favorable outcomes:
Judie wants to choose 2 miniature chocolate bars. There are 3 miniature chocolate bars in the candy dish. We can use the combination formula again to calculate the number of ways to choose 2 miniature chocolate bars out of 3:
Favorable outcomes = 3C2 = 3! / (2! * (3-2)!)
= 3! / (2! * 1!)
= 3 / 2
= 3
Probability:
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total possible outcomes
= 3 / 28
≈ 0.107 (rounded to three decimal places)
Therefore, the probability that Judie chooses 2 miniature chocolate bars is approximately 0.107.
there are 8 things in the dish to start.
She chooses the first choc with probability 2/8 or 1/4.
Now there are seven things in the dish, one of which she wants so now it is 1/7
so
(1/7)(1/4) = 1/28