During a clothing sale, 1/4 of the store merchandise is reduced in price. Find the probablility that 3 of 5 randomly-selectled shirts have reduced prices.
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Probability all 5 are reduced is
P(5) = (1/4)^5 = 0.000996
Probability that none are reduced is
P(0) = (3/4)^5 = 0.3773
Probability that 3 out of 5 are reduced is
P(3) = (1/4)^3*(3/4)^2* [5!/(2!*3!]= 0.0879
P(1) = (1/4)(3/4)^4*5 = 0.3955
P(2) = (1/4)^2*(3/4)^3*[5!/(2!*3!)] = 0.2637
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To find the probability that 3 out of 5 randomly selected shirts have reduced prices during the clothing sale, we need to use the concept of combinations.
First, let's determine the total number of ways we can select 5 shirts out of the total number of shirts in the store. Since 1/4 of the store merchandise is reduced in price, it means that 3/4 of the store merchandise is not reduced in price. Thus, the total number of ways to choose 5 shirts is given by the combination formula:
C(n, k) = n! / (k!(n-k)!)
In this case, n refers to the total number of shirts in the store (let's assume it is denoted by N), and k is the number of shirts with reduced prices we want to choose (which is 3 in this case).
Now, let's calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
The number of favorable outcomes is the number of ways we can choose 3 shirts with reduced prices out of the total number of shirts with reduced prices, which is given by the combination formula:
C(1/4 * N, 3) = (1/4 * N)! / [3! * (1/4 * N - 3)!]
Since the total number of outcomes is the number of ways we can choose 5 shirts out of the total number of shirts in the store, the total number of possible outcomes is given by the combination formula:
C(N, 5) = N! / (5! * (N - 5)!)
Finally, we can substitute the values into the probability formula:
Probability = [C(1/4 * N, 3)] / [C(N, 5)]
= [(1/4 * N)! / [3! * (1/4 * N - 3)!]] / [N! / (5! * (N - 5)!)]
Simplifying this expression gives us the probability that 3 out of 5 randomly selected shirts have reduced prices during the clothing sale.