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A jar has 5 marbles 1 of each of the colors red, white blue and yellow. If 4 marbles are removed from the jar. What is the probability that the yellow marble was removed?

A jar has 5 marbles 1 of each of the colors red, white blue and yellow. If 4 marbles are removed from the jar. What is the probability that the yellow marble was removed?

Explanation

 Let's analyze the problem:

  • Total marbles in the jar: 5 (red, white, blue, yellow, and 1 more color)

  • 4 marbles are removed.

  • Find the probability that the yellow marble was removed.

Step 1: Total ways to remove 4 marbles from 5

text{Total ways} = binom{5}{4} = 5
Step 2: Number of ways to remove 4 marbles, including yellow

To include the yellow marble, we must select the yellow marble and 3 others from the remaining 4 marbles:


text{Favorable ways} = binom{4}{3} = 4
Step 3: Probability yellow marble is removed
P = frac{text{Favorable ways}}{text{Total ways}} = frac{4}{5}