Question

Given that a survey respondent is a girl, what is the probability she prefers cats? (Round to the nearest hundredth and report as a decimal).​

Answer 1

Answer:

0.85

Step-by-step explanation:

Total Number of respondents =30

Number of Girls, n(G)=13

Number of Girls who like cats , $n(C\cap G)=11$

We want to find the conditional probability that a respondent prefers cats given that she is a girl, P(C|G).

$P(C|G)=\dfrac{P(C\cap G)}{P(G)} \\P(C\cap G)=\dfrac{n((C\cap G)}{n(S)} =\dfrac{11}{30}\\P(G)=\dfrac{n(G)}{n(S)} =\dfrac{13}{30}\\Therefore:\\P(C|G)=\dfrac{11/30}{13/30} \\P(C|G)=\dfrac{11}{13} \\\approx 0.85 (to the nearest hundredth)$