Final answer:
To find the probability of both events C and D occurring (P(C AND D)), use the formula for the union of two events. Given P(C) = 0.6, P(D) = 0.45, and P(C OR D) = 0.75, we can solve for P(C AND D), which is 0.30.
Step-by-step explanation:
To find the probability of both events C and D occurring, known as P(C AND D), we can use the formula for the union of two events, which states that the probability of the union of two events is the sum of the probabilities of each event minus the probability of their intersection.
The equation is:
P(C OR D) = P(C) + P(D) – P(C AND D)
We are given:
- P(C) = 0.6
- P(D) = 0.45
- P(C OR D) = 0.75
Substituting these values into the equation, we get:
0.75 = 0.6 + 0.45 – P(C AND D)
Solving for P(C AND D), we find:
P(C AND D) = 0.6 + 0.45 – 0.75 = 0.30
Therefore, the probability that both events C and D occur, P(C AND D), is 0.30.
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