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Given that events A and B are independent with
P(A)=0.9 and
P(B)=0.21, determine the value of
P(A and
B), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.9$ and $P(B)=0.21$ , determine the value of $P(A$ and $B)$ , 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)=0.9

and

P(B)=0.21

, determine the value of

P(A

and

B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Understand Independent Events: Understand the concept of independent events. For two independent events $A$ and $B$ , the probability of both events occurring is the product of their individual probabilities. This is expressed as: $P(A \text{ and } B) = P(A) \times P(B)$
Calculate Probability: Use the given probabilities to calculate $P(A \text{ and } B)$ . We are given: $P(A) = 0.9$ $P(B) = 0.21$ Now we calculate the probability of both events occurring: $P(A \text{ and } B) = P(A) \times P(B)$ $= 0.9 \times 0.21$
Perform Multiplication: Perform the multiplication to find the probability. $\newline$ $P(A \text{ and } B) = 0.9 \times 0.21$ $\newline$ $= 0.189$
Round Answer: Round the answer to the nearest thousandth if necessary. $\newline$ The calculated probability is already to the nearest thousandth, so no further rounding is needed.

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