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Given that events A and B are independent with
P(A)=0.3 and
P(B∣A)=0.89 determine the value of
P(B), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.3$ and $P(B \mid A)=0.89$ determine the value of $P(B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Identify independent and dependent events

Full solution

Q. Given that events A and B are independent with

P(A)=0.3

and

P(B \mid A)=0.89

determine the value of

P(B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Define Independent Events: Since events $A$ and $B$ are independent, the probability of $B$ occurring is not affected by the occurrence of $A$ . Therefore, $P(B|A)$ is the same as $P(B)$ . We can use the definition of independent events to find $P(B)$ .
Calculate Probability of Both Events: For independent events $A$ and $B$ , the probability of both $A$ and $B$ occurring is the product of their individual probabilities: $P(A \text{ and } B) = P(A) \times P(B)$ .
Given Probabilities: We are given $P(A) = 0.3$ and $P(B|A) = 0.89$ . Since $A$ and $B$ are independent, $P(B|A) = P(B)$ . Therefore, we can equate $P(B)$ to $0.89$ .
Final Probability Calculation: We have determined that $P(B) = 0.89$ . This is the probability of event $B$ occurring, rounded to the nearest thousandth as required.

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