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 target

The problem can be solved by calculating the individual probabilities of each person hitting the target and then using the formula for the probability of at least one event occurring.

1. Calculate the individual probabilities:

   • Ramu's probability of hitting the target is 3/6 = 0.5
   • Siva's probability of hitting the target is 2/6 = 0.33
   • Shyam's probability of hitting the target is 4/4 = 1

2. Calculate the probability of at least one person hitting the target:

   • The formula for the probability of at least one event occurring is 1 - the probability of none of the events occurring.
   • The probability of none of the events occurring is the product of the probabilities of each event not occurring.
   • The probability of Ramu not hitting the target is 1 - 0.5 = 0.5
   • The probability of Siva not hitting the target is 1 - 0.33 = 0.67
   • The probability of Shyam not hitting the target is 1 - 1 = 0
   • The probability of none of them hitting the target is 0.5 * 0.67 * 0 = 0
   • Therefore, the probability of at least one person hitting the target is 1 - 0 = 1

3. Calculate the probability of at least two people hitting the target:

   • This is a bit more complicated because it involves combinations of events.
   • We need to calculate the probability of each possible combination of two people hitting the target and then add those probabilities together.
   • The possible combinations are: Ramu and Siva, Ramu and Shyam, and Siva and Shyam.
   • The probability of Ramu and Siva both hitting the target is 0.5 * 0.33 = 0.165
   • The probability of Ramu and Shyam both hitting the target is 0.5 * 1 = 0.5
   • The probability of Siva and Shyam both hitting the target is 0.33 * 1 = 0.33
   • The total probability of at least two people hitting the target is 0.165 + 0.5 + 0.33 = 0.995

So, the probability that at least 2 shots hit the target is approximately 0.995 or 99.5%.