Allison has a pouch of 6 pink marbles, 4 blue marbles, and 8 white marbles.What is the probability that the first marble is blue and the second marble is white if replacement is allowed?*1 pointA. 0.078B. 0.099C. 0.104D. 0.148
Question
Allison has a pouch of 6 pink marbles, 4 blue marbles, and 8 white marbles.What is the probability that the first marble is blue and the second marble is white if replacement is allowed?*1 pointA. 0.078B. 0.099C. 0.104D. 0.148
Solution
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.
In this case, the total number of marbles is 6 (pink) + 4 (blue) + 8 (white) = 18 marbles.
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The probability that the first marble drawn is blue is calculated as follows: Number of blue marbles / Total number of marbles = 4/18 = 0.222
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Since replacement is allowed, the total number of marbles remains the same for the second draw. The probability that the second marble drawn is white is calculated as follows: Number of white marbles / Total number of marbles = 8/18 = 0.444
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Since these are independent events (drawing the first marble does not affect the probability of drawing the second marble), the probability of both events occurring is the product of their individual probabilities.
So, the probability that the first marble is blue and the second marble is white is 0.222 * 0.444 = 0.099
Therefore, the answer is B. 0.099.
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