Question

An urn contains 10 red marbles, 9 white marbles, and 7 blue marbles. A child randomly selects three marbles from the urn without replacement. What is the probability that all three marbles are red? Round to four decimal places.

Answer 1

The probability of drawing three red marbles without replacement from the urn is 0.0434.

Step-by-step explanation:

To find the probability that all three marbles are red, we need to calculate the probability of drawing a red marble on the first draw, and then the conditional probability of drawing another red marble on the second draw, given that the first marble was red. Finally, we calculate the conditional probability of drawing a third red marble, given that the first two marbles were red.

The probability of drawing a red marble on the first draw is 10/26. After removing a red marble, the probability of drawing another red marble on the second draw is 9/25. And after removing two red marbles, the probability of drawing a third red marble on the third draw is 8/24.

To find the probability of all three events occurring together, we multiply the individual probabilities: (10/26) * (9/25) * (8/24) = 0.0434.