Question

g.pr.10.1 (mc)

find p(b | a). are events a and b independent?

a and b events

	a	not a	total
not b	90	60	150
total	300	200	500

Explanation:

Calculate the conditional probability \(P(B \mid A)\)

$$ P(B \mid A) = \frac{n(A \text{ and } B)}{n(A)} = \frac{210}{300} = 0.7 $$

Calculate the marginal probability \(P(B)\)

$$ P(B) = \frac{n(B)}{\text{Total}} = \frac{350}{500} = 0.7 $$

Determine independence by comparing \(P(B \mid A)\) and \(P(B)\)

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Answer:

\(P(B \mid A) = 0.7\); Yes, events \(A\) and \(B\) are independent.