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Given
P(A)=0.74,P(B)=0.6 and
P(A∣B)=0.9, find the value of
P(A and
B), rounding to the nearest thousandth, if necessary.
Answer:

Given $P(A)=0.74, P(B)=0.6$ and $P(A \mid B)=0.9$ , find the value of $P(A$ and $B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Given

P(A)=0.74, P(B)=0.6

and

P(A \mid B)=0.9

, find the value of

P(A

and

B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Define conditional probability: Understand the definition of conditional probability. The conditional probability $P(A|B)$ is defined as the probability of event $A$ occurring given that event $B$ has occurred. The formula for conditional probability is $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$ . We can rearrange this formula to solve for $P(A \text{ and } B)$ by multiplying both sides by $P(B)$ .
Calculate $P(A \text{ and } B)$ : Calculate the value of $P(A \text{ and } B)$ . Using the formula from Step $1$ , we have $P(A|B) \times P(B) = P(A \text{ and } B)$ . We know that $P(A|B) = 0.9$ and $P(B) = 0.6$ . So, $P(A \text{ and } B) = 0.9 \times 0.6$ .
Perform multiplication: Perform the multiplication to find $P(A \text{ and } B)$ . $\newline$ $P(A \text{ and } B) = 0.9 \times 0.6 = 0.54$ .
Round answer: Round the answer to the nearest thousandth if necessary. $\newline$ Since the answer is already at the thousandth place, no rounding is necessary.

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