Find the probability selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles when (a) you replace the first marble before drawing the second, and (b) you do not replace the first marble. Then, compare the probabilities. Round your answers to four decimal places.

Question

Mathematics

Lukas Scott

27 December, 17:36

Find the probability selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles when (a) you replace the first marble before drawing the second, and (b) you do not replace the first marble. Then, compare the probabilities. Round your answers to four decimal places.

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Answers (1)

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Armando Sweeney · Answer 1

Step-by-step explanation:

There are a total of 16 marbles, 8 of which are green.

(a) The probability the first marble is green is 8/16.

The marble is replaced, so there are still a total of 15 marbles, 8 of which are green. The probability the second marble is green is 8/16.

The probability of both events is (8/16) (8/16) = 1/4 = 0.2500.

(b) The probability the first marble is green is 8/16.

The marble is not replaced, so there are now a total of 15 marbles, 7 of which are green. The probability the second marble is green is 7/15.

The probability of both events is (8/16) (7/15) = 7/30 = 0.2333.