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Given that events A and B are independent with
P(A)=0.6 and
P(B)=0.72, determine the value of
P(A nn B), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.6$ and $P(B)=0.72$ , determine the value of $P(A \cap B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Identify independent events

Full solution

Q. Given that events A and B are independent with

P(A)=0.6

and

P(B)=0.72

, determine the value of

P(A \cap B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Use Multiplication Rule: To find the probability of both independent events $A$ and $B$ occurring together, we use the multiplication rule for independent events. The rule states that $P(A \cap B) = P(A) \times P(B)$ .
Calculate $P(A \cap B)$ : Now we calculate $P(A \cap B)$ using the given probabilities $P(A) = 0.6$ and $P(B) = 0.72$ . $\newline$ $P(A \cap B) = 0.6 \times 0.72$
Perform Multiplication: Performing the multiplication, we get: $P(A \cap B) = 0.432$
Check Result: Since the problem asks for the answer rounded to the nearest thousandth if necessary, we check our result. The value $0.432$ is already rounded to the nearest thousandth, so no further action is needed.

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