Question

In a shooting test, the probability of hitting the target is 1/2 for a, 2/3 for b, and 3/4 for c. What is the probability that all of them hit the target?

Answer 1

The probability that all three individuals, each with different chances of hitting a target, will all hit the target is found by multiplying their individual probabilities. The result is 1/4, meaning there is a 25% chance they all hit the target.

Step-by-step explanation:

The question asks for the probability that three individuals (a, b, and c), each with different probabilities of hitting a target, all hit the target. The probability of 'a' hitting the target is 1/2, 'b' is 2/3, and 'c' is 3/4. To find the probability that all of them hit the target, you multiply these probabilities together because the events are independent.

Here's the calculation:

• P(a hits) = 1/2
• P(b hits) = 2/3
• P(c hits) = 3/4

So the combined probability of all hitting the target is P(a) × P(b) × P(c) = (1/2) × (2/3) × (3/4).

Let's do the math:

1. First, calculate 1/2 × 2/3 = 1/3.
2. Then, multiply the result by 3/4: 1/3 × 3/4 = 1/4.

Therefore, the probability that all three individuals hit the target is 1/4, or 0.25, which means there is a 25% chance that all three will hit the target on their turns.