Answer: C- 42.1%
Step-by-step explanation:
Let H represents the event of liking hotdogs, B represents the event of liking burger and S represents total number of students,
Thus, by the given table,
n(H) = 76, n(S) = 150, [tex]n(H\cap B) = 32[/tex]
⇒ [tex]P(H)=\frac{n(H)}{n(S)}=\frac{76}{150}[/tex]
Also,
[tex]P(H\cap B) = \frac{n(H\cap B)}{n(S)}= \frac{32}{150}[/tex]
Thus, by the definition of conditional probability,
The probability of liking burger when it is given that the student likes the hotdgs,
[tex]P(\frac{B}{H})=\frac{P(H\cap B)}{P((H)}[/tex]
[tex]=\frac{32/150}{76/150}[/tex]
[tex]=\frac{32}{76}[/tex]
[tex]=0.421052632[/tex]
[tex]=42.1052632\%\approx 42.1\%[/tex]
⇒ Option C is correct.
