A problem is given to three persons P, Q, R whose respective chances of solving it are 2/7, 4/7, 4/9 respectively. What is the probability that the problem is solved?Choices:- 122/147 25/147 120/147 117/147

The problem can be solved by using the formula of probability:

P(E) = P(E1) + P(E2) + P(E3) - P(E1 ∩ E2) - P(E1 ∩ E3) - P(E2 ∩ E3) + P(E1 ∩ E2 ∩ E3)

Where:

• E is the event that the problem is solved.
• E1 is the event that person P solves the problem.
• E2 is the event that person Q solves the problem.
• E3 is the event that person R solves the problem.

Given that the chances of P, Q, R solving the problem are 2/7, 4/7, 4/9 respectively, we can substitute these values into the formula:

P(E) = 2/7 + 4/7 + 4/9 - (2/7 * 4/7) - (2/7 * 4/9) - (4/7 * 4/9) + (2/7 * 4/7 * 4/9)

Solving this equation gives us the probability that the problem is solved.

Please note that the events E1, E2, and E3 are independent, meaning the probability of one event occurring does not affect the probability of the other events occurring. This is why we can use the formula in this way.

To solve this problem, we need to find the probability that at least one of them solves the problem. This is equal to 1 minus the probability that none of them solves the problem.

The probability that P does not solve the problem is 1 - 2/7 = 5/7. The probability that Q does not solve the problem is 1 - 4/7 = 3/7. The probability that R does not solve the problem is 1 - 4/9 = 5/9.

The probability that none of them solves the problem is the product of their individual probabilities of not solving the problem, which is (5/7) * (3/7) * (5/9) = 75/441.

Therefore, the probability that at least one of them solves the problem is 1 - 75/441 = 366/441 = 122/147.

So, the correct answer is 122/147.

The problem can be solved by using the formula of probability:

P(E) = P(E1) + P(E2) + P(E3) - P(E1 ∩ E2) - P(E1 ∩ E3) - P(E2 ∩ E3) + P(E1 ∩ E2 ∩ E3)

Where:

• P(E) is the probability that the problem is solved.
• P(E1), P(E2), and P(E3) are the probabilities that P, Q, and R solve the problem, respectively.
• P(E1 ∩ E2), P(E1 ∩ E3), and P(E2 ∩ E3) are the probabilities that two of the three people solve the problem.
• P(E1 ∩ E2 ∩ E3) is the probability that all three people solve the problem.

Given that the chances of P, Q, and R solving the problem are 2/7, 4/7, and 4/9 respectively, we can substitute these values into the formula:

P(E) = 2/7 + 4/7 + 4/9 - (2/7 * 4/7) - (2/7 * 4/9) - (4/7 * 4/9) + (2/7 * 4/7 * 4/9)

Solving this equation gives us the probability that the problem is solved. The correct answer is 120/147.