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ehidna [41]
3 years ago
14

If A and B are events with P(A) = 0.5, P(A OR B) = 0.65, P(A AND B) = 0.15, find P(B).

Mathematics
1 answer:
sleet_krkn [62]3 years ago
3 0

Answer:

P(B) = 0.30

Step-by-step explanation:

This is a probability problem that can be modeled by a diagram of Venn.

We have the following probabilities:

P(A) = P_{A} + P(A \cap B) = 0.50

In which P_{A} is the probability that only A happens.

P(B) = P_{B} + P(A \cap B) = P_{B} + 0.15

To find P(B), first we have to find P_{B}, that is the probability that only B happens.

Finding P_{B}:

The problem states that P(A OR B) = 0.65. This is the probability that at least one of this events happening. Mathematically, it means that:

1) P_{A} + P(A \cap B) + P_{B} = 0.65

The problem states that P(A) = 0.5 and P(A \cap B) = 0.15. So we can find P_{A}.

P(A) = P_{A} + P(A \cap B)

0.5 = P_{A} + 0.15

P_{A} = 0.35

Replacing it in equation 1)

P_{A} + P(A \cap B) + P_{B} = 0.65

0.35 + 0.15 + P_{B} = 0.65

P_{B} = 0.65 - 0.35 - 0.15

P_{B} = 0.15

Since

P(B) = P_{B} + P(A \cap B)

P(B) = 0.15 + 0.15

P(B) = 0.30

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