Question

g.pr.10.1 (mc)

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

\\(\

$$\begin{array}{c|c|c|c} & a & \\text{not } a & \\text{total} \\\\ \\hline b & 275 & 105 & 380 \\\\ \\hline \\text{not } b & 25 & 95 & 120 \\\\ \\hline \\text{total} & 300 & 200 & 500 \\end{array}$$

\\)

• 0.82; yes
• 0.7; no
• 0.92; no
• 0.7; yes

Explanation:

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

$$ P(B \mid A) = \frac{n(A \cap B)}{n(A)} = \frac{275}{300} \approx 0.9167 \approx 0.92 $$

Determine independence of events A and B

$$
LATEXBLOCK0
$$

Answer:

• 0.82; Yes
• 0.7; No
• 0.92; No (Correct answer)
• 0.7; Yes