Answer :
Final answer:
To find the total number of counters in the bag, we set up an equation using the given probabilities and solve for x. The solution is x = 24 and the total number of counters is 34.
Explanation:
Let the number of blue counters be x.
Since there are 10 red counters and x blue counters in the bag, the total number of counters is 10 + x.
The probability that the first counter drawn is blue is x/(10 + x). Since one blue counter has been removed, there are now x - 1 blue counters left. Therefore, the probability that the second counter drawn is blue is (x - 1)/(9 + x).
According to the problem, the probability that both counters drawn are blue is 1/8. So we can write the equation: x/(10 + x) * (x - 1)/(9 + x) = 1/8.
Simplifying the equation and solving for x, we find that x = 24.
Therefore, the total number of counters is 10 + 24 = 34.
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