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 targetOptions5/21/35/62/3

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 be calculated by adding the probabilities of exactly 2, 3, and 4 shots hitting the target.

The probability of exactly 2 shots hitting the target can be calculated by multiplying the probabilities of two people hitting the target and one person missing. There are three possible combinations for this: RAMU and SIVA hit, RAMU and SHYAM hit, or SIVA and SHYAM hit.

The probability of exactly 3 shots hitting the target can be calculated by multiplying the probabilities of three people hitting the target. There is only one possible combination for this: RAMU, SIVA, and SHYAM all hit.

The probability of all 4 shots hitting the target is simply the probability of SHYAM hitting the target, which is 1.

Adding these probabilities together, we get the total probability that at least 2 shots hit the target.

However, the problem does not provide enough information to calculate these probabilities. We would need to know the correlation between the shots (i.e., whether they are independent or dependent events) in order to calculate the exact probabilities.

Without this information, we cannot determine the correct answer from the provided options.

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: The probability is 0.5 * 0.33 = 0.165.
• Ramu and Shyam hit the target: The probability is 0.5 * 1 = 0.5.
• Siva and Shyam hit the target: The probability is 0.33 * 1 = 0.33.
• All three hit the target: The probability is 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 suggests that there might be some overlap in the events, meaning that the same outcome is being counted more than once.

Without more information about the problem, it's difficult to provide a more accurate answer. The options provided (5/2, 1/3, 5/6, 2/3) do not include 1.16, suggesting that the problem may need to be approached in a different way or that there may be a mistake in the problem or the options.