Question

Let A, B and C be independent events with P(A) = 0.5, P(B) =

0.9, and P(C) = 0.3. Find P(A and B and C).

Answer 1

The probability of independent events A, B, and C all occurring together, P(A and B and C), is found by multiplying their probabilities: 0.5 × 0.9 × 0.3, which equals 0.135.

Step-by-step explanation:

To find the probability of independent events A, B, and C all occurring, denoted by P(A and B and C), you simply multiply their individual probabilities:

• P(A) = 0.5
• P(B) = 0.9
• P(C) = 0.3

So, P(A and B and C) = P(A) × P(B) × P(C).
Using the values provided:

P(A and B and C) = 0.5 × 0.9 × 0.3 = 0.135.

Hence, the probability of A, B, and C all happening together is 0.135.