Question

Probability of event a is 0.4 and probability of event b is 0.5. p (a/b) = 0.3. find p(a ∩ b)? 0.15

Answer 1

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Answer 2

Answer:

ANSWER :

What is the probability of event A if A and B are independent events with P(A)=P(B) and p(AUB)=0.5?

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We can use the fact that there are two formulas for P(A and B). One is always true and one is only true if A and B are independent.

Always true: P(A and B) = P(A) + P(B) - P(A or B)

If A and B are independent: P(A and B) = P(A)*P(B)

We’re also given that P(A)=P(B), so we can substitute P(A) whenever there’s a P(B) and set these two formulas equal to each other. We were also given that P(A or B) = .5

Now we have P(A)^2 = 2P(A) - 0.5

We can solve for P(A) now using the quadratic formula and we find that it is approximately 0.2929....

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