Question

C and D are events with probabilities P(C)=0.15,P(D)=0.3, and P(C UD)=0.35. Find P(C∣D), the conditional probability that C happens, given that we know D happened.

Answer 1

To find the conditional probability that event C happens given that event D has happened (P(C|D)), we calculate P(C AND D) / P(D) which comes out to be approximately 0.333.

Step-by-step explanation:

To find the conditional probability P(C|D) of event C happening given that D has happened, we use the formula P(C|D) = P(C AND D) / P(D). Given P(C)=0.15, P(D)=0.3, and P(C UD)=0.35, we first need to find P(C AND D).

To determine P(C AND D), we can use the formula P(C UD) = P(C) + P(D) - P(C AND D) and solve for P(C AND D). Plugging in the given values:

P(C UD) = 0.35

P(C) + P(D) = 0.15 + 0.3 = 0.45

Therefore, P(C AND D) = P(C) + P(D) - P(C UD) = 0.45 - 0.35 = 0.1

Now, we can find the conditional probability P(C|D) by dividing P(C AND D) by P(D): P(C|D) = P(C AND D) / P(D) = 0.1 / 0.3 = 0.333...

So, the conditional probability that C happens given D has happened is approximately 0.333.