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Question

A jar contains seven blue marbles and four red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event. Both of the selected marbles are red.

The probability that both of the selected marbles are red is =

(Round to three decimal places as needed.)

Answer 1

First, let's find the probability of selecting a red marble on the first draw:

Probability of selecting a red marble on the first draw = Number of red marbles / Total number of marbles
= 4 / (7 + 4)
= 4 / 11

Since we do not replace the marble after the first draw, there will now be 3 red marbles and a total of 10 marbles left in the jar for the second draw.

Probability of selecting a red marble on the second draw = Number of remaining red marbles / Total number of remaining marbles
= 3 / 10

To find the probability of both selected marbles being red, we multiply the probabilities of the two events:

Probability = (4/11) * (3/10)
= 12 / 110
= 0.109

Therefore, the probability that both selected marbles are red is 0.109 or 10.9%.