Three children took part in racing competition in their school with their respective probabilities to reach the finishing point being 1/3, 1/5 and 1/4 respectively. What is the probability that at least one of them will finish the race?
Question
Three children took part in racing competition in their school with their respective probabilities to reach the finishing point being 1/3, 1/5 and 1/4 respectively. What is the probability that at least one of them will finish the race?
Solution
To solve this problem, it's easier to find the probability that none of them will finish the race and then subtract that from 1.
The probability that the first child will not finish the race is 1 - 1/3 = 2/3. The probability that the second child will not finish the race is 1 - 1/5 = 4/5. The probability that the third child will not finish the race is 1 - 1/4 = 3/4.
The probability that none of them will finish the race is the product of these probabilities, which is (2/3) * (4/5) * (3/4) = 8/15.
Therefore, the probability that at least one of them will finish the race is 1 - 8/15 = 7/15.
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