A bag contains 2 red, 4 yellow, and 6 blue marbles. Two marbles are drawn at random. Find the probability that both are blue.
Answer (2)
The question asks for the probability of drawing two blue marbles in a row from a bag containing 2 red, 4 yellow, and 6 blue marbles, without replacement. To solve this, we understand that the probability of drawing a blue marble on the first draw is 6/12 (since there are 6 blue marbles out of 12 total marbles). If a blue marble is drawn first, it is not replaced, so the probability of drawing another blue marble is 5/11 (since now there are 5 blue marbles out of 11 total marbles). Therefore, the probability of drawing two blue marbles in a row is calculated by multiplying these probabilities: 6/12 * 5/11 = 30/132 or 5/22.
The probability of drawing two blue marbles from the bag is 22 5 . This is calculated by first finding the probability of drawing a blue marble on the first draw and then the second draw without replacement. Therefore, the combined probability is 2 1 × 11 5 = 22 5 .
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