Three students are working independently on a Mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. What is the p...

Three students are working independently on a Mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. What is the probability that at least one of them solves the problem?

Answer Details

To find the probability that at least one of the three students solves the problem, we need to calculate the probability that none of them solve the problem and then subtract that from 1 (which represents the total probability). The probability that the first student does not solve the problem is 0.4 (since the probability of solving the problem is 0.6). Similarly, the probability that the second student does not solve the problem is 0.3 and the probability that the third student does not solve the problem is 0.2. To find the probability that none of them solve the problem, we multiply these probabilities together: 0.4 x 0.3 x 0.2 = 0.024. Therefore, the probability that at least one of the three students solves the problem is 1 - 0.024 = 0.976. So, the correct answer is: 0.976.