Introduction to Probability: 4600 Solved Problems and Practice Exercises Involving Dice, Marbles, Coins, and More! by Dorothy Stein

Author:Dorothy Stein [Stein, Dorothy]
Language: eng
Format: azw3, epub
Published: 2021-05-13T16:00:00+00:00

162. Two marbles are drawn at random, one after the other, without replacement, from a bag that contains 14 red, 5 blue, and 22 green marbles. What is the probability that both marbles are blue?

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Solution: The probability that the first marble drawn is blue is first calculated. In the bag, initially, there are 5 blue marbles. Initially, there are 41 total marbles. Therefore, the probability that the first marble drawn is blue is 5 / 41.

After the first marble is removed, there are 4 blue marbles remaining. And the total number of marbles left in the bag is 40. Hence, the probability of drawing a blue marble the second time is 1 / 10.

Finally, the probability that both marbles are blue is just the product of these probabilities. Hence, the probability that both marbles are blue is (5 / 41) x (1 / 10) = 1 / 82.

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