Select the correct answerA box contains 3 red and 5 blue marbles. A marble is selected at random and its color is noted. The marble is then replaced in the box along with 2 more marbles of the same color. A second marble is then selected at random. What is the probability that the second marble is blue?Options 49 59 827
Question
Select the correct answerA box contains 3 red and 5 blue marbles. A marble is selected at random and its color is noted. The marble is then replaced in the box along with 2 more marbles of the same color. A second marble is then selected at random. What is the probability that the second marble is blue?Options 49 59 827
Solution
The problem can be solved in two steps:
Step 1: Calculate the total number of marbles after the first draw and replacement. Initially, there are 3 red and 5 blue marbles, making a total of 8 marbles. After the first draw, 2 more marbles of the same color are added. So, the total number of marbles becomes 8 + 2 = 10 marbles.
Step 2: Calculate the probability of drawing a blue marble the second time. After the first draw and replacement, there could be either 7 blue marbles (if a blue marble was drawn first) or 5 blue marbles (if a red marble was drawn first). The probability of drawing a blue marble first is 5/8, and the probability of drawing a red marble first is 3/8. So, the total probability of drawing a blue marble the second time is:
(Probability of blue first * Probability of blue second given blue first) + (Probability of red first * Probability of blue second given red first)
= (5/8 * 7/10) + (3/8 * 5/10)
= 35/80 + 15/80
= 50/80
= 5/8
So, the correct answer is not in the options given. The probability that the second marble is blue is 5/8.
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