RAMU can hit a target 3 times in 6 shots, SIVA can hit the target 2 times in 6 shots and SHYAM can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the targetOptions5/62/35/21/3

The problem is asking for the probability that at least 2 shots hit the target. This means we need to find the probability that either 2, 3, or all 4 shots hit the target.

First, let's calculate the individual probabilities for each person:

1. RAMU: He can hit the target 3 times in 6 shots. So, the probability of RAMU hitting the target is 3/6 = 0.5.

2. SIVA: He can hit the target 2 times in 6 shots. So, the probability of SIVA hitting the target is 2/6 = 0.33.

3. SHYAM: He can hit the target 4 times in 4 shots. So, the probability of SHYAM hitting the target is 4/4 = 1.

Next, we need to find the probability that at least 2 shots hit the target. This can happen in several ways:

• RAMU and SIVA hit the target
• RAMU and SHYAM hit the target
• SIVA and SHYAM hit the target
• All three hit the target

We can calculate these probabilities as follows:

• RAMU and SIVA: 0.5 * 0.33 = 0.165
• RAMU and SHYAM: 0.5 * 1 = 0.5
• SIVA and SHYAM: 0.33 * 1 = 0.33
• All three: 0.5 * 0.33 * 1 = 0.165

Adding these probabilities together gives us the total probability that at least 2 shots hit the target:

0.165 + 0.5 + 0.33 + 0.165 = 1.16

However, this number is greater than 1, which is not possible for a probability. This is because we have double-counted some scenarios where more than two people hit the target.

The correct way to solve this problem is to use the principle of inclusion and exclusion:

• First, add the probabilities for each pair of people: 0.165 (RAMU and SIVA) + 0.5 (RAMU and SHYAM) + 0.33 (SIVA and SHYAM) = 0.995
• Then, subtract the probability that all three people hit the target: 0.995 - 0.165 = 0.83

So, the probability that at least 2 shots hit the target is 0.83, or approximately 5/6. This is not one of the options given in the problem, so there may be a mistake in the problem or in my calculations.