Three persons Pardhu, Qureshi and Rajesh independently try to hit a target. If the probabilities of them hitting the target are 1/4, 2/3 and 5/12, respectively, then the probability that the target is hit by Qureshi or Rajesh but Not by Pardhu is:

To solve this problem, we need to use the rules of probability.

Step 1: Identify the probabilities given in the problem.

• The probability of Pardhu hitting the target, P(P) = 1/4
• The probability of Qureshi hitting the target, P(Q) = 2/3
• The probability of Rajesh hitting the target, P(R) = 5/12

Step 2: We are asked to find the probability that the target is hit by Qureshi or Rajesh but not by Pardhu. This can be written as P(Q or R and not P).

Step 3: According to the rules of probability, P(Q or R and not P) = P(Q and not P) + P(R and not P) - P(Q and R and not P)

Step 4: We can calculate these probabilities as follows:

• P(Q and not P) = P(Q) * (1 - P(P)) = 2/3 * (1 - 1/4) = 2/3 * 3/4 = 1/2
• P(R and not P) = P(R) * (1 - P(P)) = 5/12 * (1 - 1/4) = 5/12 * 3/4 = 5/16
• P(Q and R and not P) = P(Q) * P(R) * (1 - P(P)) = 2/3 * 5/12 * (1 - 1/4) = 5/36 * 3/4 = 5/48

Step 5: Substitute these values into the equation from step 3 to get the final answer: P(Q or R and not P) = 1/2 + 5/16 - 5/48 = 24/48 + 15/48 - 5/48 = 34/48 = 17/24

So, the probability that the target is hit by Qureshi or Rajesh but not by Pardhu is 17/24.