Thank you for visiting In a shooting competition the probability of a man hitting a target is 1 5 if he shoots 5 times what is the probability of. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The probability of a man hitting a target at least twice in five shots, with each shot having a 1/5 chance of success, can be calculated using the binomial probability formula and summing the individual probabilities for 2, 3, 4, or 5 successful hits.
To calculate the probability of a man hitting a target at least twice when shooting five times, given a hit probability of 1/5, we need to consider all possible scenarios where he hits 2 or more times.
Firstly, we define the event of hitting the target as a 'success' and not hitting as a 'failure'. The man's probability of 'failure' is 4/5.
We will use the binomial probability formula: P(X = k) = C(n, k) * (p^k) * ((1 - p)^(n - k)), where P(X = k) is the probability of k successes in n trials, C(n, k) is the number of combinations, and p is the probability of success on a single trial.
The probability of hitting the target at least twice (2, 3, 4, or 5 times) is the sum of the individual probabilities of hitting it exactly 2, 3, 4, or 5 times. This sum can be calculated as follows:
- Probability of hitting exactly 2 times: C(5, 2) * (1/5)^2 * (4/5)^3
- Probability of hitting exactly 3 times: C(5, 3) * (1/5)^3 * (4/5)^2
- Probability of hitting exactly 4 times: C(5, 4) * (1/5)^4 * (4/5)^1
- Probability of hitting exactly 5 times: C(5, 5) * (1/5)^5 * (4/5)^0
Add all the probabilities for 2, 3, 4, and 5 hits to find the combined probability of hitting the target at least twice.
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