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Chapter 11: Problem 17

Use the fact that we have independent events \(\mathrm{A}\) and \(\mathrm{B}\) with \(P(A)=0.7\) and \(P(B)=0.6\). Find \(P(A\) and \(B)\).

Short Answer

Expert verified
The probability of both events A and B occurring is 0.42.

Step by step solution

01

Identifying the given probabilities

The probability of event A, denoted as \(P(A)\), is given as 0.7 and the probability of event B, denoted as \(P(B)\), is given as 0.6.
02

Using the multiplication rule for independent events

With the knowledge that events A and B are independent, the principle of multiplication for independent events can be applied. According to this principle, the probability of both events A and B occurring, denoted as \(P(A \cap B)\), is computed by multiplying the probability of event A by the probability of event B. Mathematically, this can be expressed as \(P(A \cap B) = P(A)*P(B)\).
03

Calculating the result

Substituting the given probabilities into the formula will give \(P(A \cap B) = 0.7 * 0.6 = 0.42\).

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