Question

Suppose F and G are independent events. If P(F) = 0.25 and P(G) = 0.06, then what is P (F and G)? Keep all digits. Don't round. Suppose H and J are disjoint events. If P(H) = 0.24 and P(J) = 0.33, then what is P (H or J)? Keep all digits. Don't round.

Answer 1

The probability of independent events F and G both occurring, P(F AND G), is 0.015. The probability of either disjoint events H or J occurring, P(H OR J), is 0.57.

Step-by-step explanation:

If F and G are independent events, the probability of both events occurring is calculated by multiplying the probabilities of each event. Therefore, to find P(F AND G), you would calculate:

P(F AND G) = P(F) × P(G) = 0.25 × 0.06 = 0.015

Disjoint events, also known as mutually exclusive events, cannot happen at the same time. The probability of either H or J occurring is the sum of their individual probabilities, since no overlap exists. Therefore, to find P(H OR J), you would calculate:

P(H OR J) = P(H) + P(J) = 0.24 + 0.33 = 0.57