Question

An urn contains 10 green and 5 red marbles. Four marbles are randomly selected (without replacement). Find the probabilities that exactly 0, 1, 2, 3 or 4 red marbles have been selected.

Answer 1

To calculate the probabilities of selecting 0, 1, 2, 3, or 4 red marbles, we use combinations to calculate the number of ways to choose the marbles and then divide it by the total number of ways to choose any 4 marbles from the urn.

Step-by-step explanation:

To calculate the probabilities, we can use the concept of combinations. The total number of marbles in the urn is 15 (10 green + 5 red). For each scenario (0, 1, 2, 3, 4 red marbles selected), we calculate the number of ways to choose the red marbles and green marbles, and then divide it by the total number of ways to choose any 4 marbles from the urn.

Let's calculate the probability for each scenario:

Probability of exactly 0 red marbles: P(0 red) = C(10, 4)/C(15, 4)

Probability of exactly 1 red marble: P(1 red) = C(5, 1) * C(10, 3)/C(15, 4)

Probability of exactly 2 red marbles: P(2 red) = C(5, 2) * C(10, 2)/C(15, 4)

Probability of exactly 3 red marbles: P(3 red) = C(5, 3) * C(10, 1)/C(15, 4)

Probability of exactly 4 red marbles: P(4 red) = C(5, 4)/C(15, 4)