use the venn diagram to calculate probabilities. which probability is correct? o $p(a|b)=\frac{1}{2}$ o…

Explanation:

Step1: Recall conditional - probability formula

$P(X|Y)=\frac{P(X\cap Y)}{P(Y)}$

Step2: Calculate $n(A)$

$n(A)=3 + 1+7 + 6=17$

Step3: Calculate $n(B)$

$n(B)=1 + 9+6 + 4=20$

Step4: Calculate $n(C)$

$n(C)=7 + 6+4 + 6=23$

Step5: Calculate $n(A\cap B)$

$n(A\cap B)=1 + 6=7$

Step6: Calculate $n(A\cap C)$

$n(A\cap C)=7 + 6=13$

Step7: Calculate $n(B\cap C)$

$n(B\cap C)=6 + 4=10$

Step8: Calculate $n(A\cap B\cap C)$

$n(A\cap B\cap C)=6$

Step9: Calculate $P(A|B)$

$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{7}{20}$

Step10: Calculate $P(B|A)$

$P(B|A)=\frac{n(A\cap B)}{n(A)}=\frac{7}{17}$

Step11: Calculate $P(A|C)$

$P(A|C)=\frac{n(A\cap C)}{n(C)}=\frac{13}{23}$

Step12: Calculate $P(C|A)$

$P(C|A)=\frac{n(A\cap C)}{n(A)}=\frac{13}{17}$

Answer:

$P(C|A)=\frac{13}{17}$