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

0.85

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