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Novosadov [1.4K]
3 years ago
14

Given the following probabilities, for what P(B) are events A and B independent?

Mathematics
1 answer:
AlexFokin [52]3 years ago
5 0

Answer: the value of P(B) = \dfrac{1}{3} .

Step-by-step explanation:

If A and B are two independent events, then P(A and B)=P(A) x P(B)  (i)

Given the following probabilities : P(A)=\dfrac{1}{2},\  \ P(\text{A and B})=\dfrac{1}{6}

To find : P(B) such that events A and B are independent

Put all values in (i), we get

\dfrac{1}{6}=\dfrac{1}{2}\times P(B)\\\\\Rightarrow\ P(B)=\dfrac{2}{6}\\\\\Rightarrow\ P(B)=\dfrac{1}{3}

Hence, the value of P(B) = \dfrac{1}{3} .

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