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?
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?
Solution
Step 1: Identify the total number of marbles. Initially, there are 3 red and 5 blue marbles, so there are 8 marbles in total.
Step 2: Calculate the probability of selecting a blue marble the first time. This is the number of blue marbles divided by the total number of marbles, which is 5/8.
Step 3: If a blue marble is selected, 2 more blue marbles are added to the box. So, the total number of marbles becomes 10 and the number of blue marbles becomes 7.
Step 4: Calculate the probability of selecting a blue marble the second time. This is the new number of blue marbles divided by the new total number of marbles, which is 7/10.
Step 5: The probability that the second marble is blue, given that the first marble was blue and was replaced along with 2 more blue marbles, is 7/10.
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