To determine the probability that a student likes both hotdogs and burgers given that they like hotdogs, we need to follow these steps:
1. Identify the number of students who like both hotdogs and burgers.
From the table, we see that there are 32 students who like both hotdogs and burgers.
2. Identify the total number of students who like hotdogs.
From the table, we see that there are 76 students who like hotdogs (this includes both those who like burgers and those who do not).
3. Calculate the probability.
The probability that a student likes burgers given that they like hotdogs is given by the ratio of the number of students who like both hotdogs and burgers to the total number of students who like hotdogs.
So, the probability [tex]\( P(\text{Likes Burgers | Likes Hotdogs}) \)[/tex] is:
[tex]\[
P(\text{Likes Burgers | Likes Hotdogs}) = \frac{\text{Number of students who like both hotdogs and burgers}}{\text{Total number of students who like hotdogs}}
\][/tex]
Plugging in the numbers from above:
[tex]\[
P(\text{Likes Burgers | Likes Hotdogs}) = \frac{32}{76}
\][/tex]
4. Convert the probability to a percentage.
[tex]\[
P(\text{Likes Burgers | Likes Hotdogs}) \times 100 = \left( \frac{32}{76} \right) \times 100 \approx 42.11\%
\][/tex]
Thus, the probability that a student likes burgers given that they like hotdogs is approximately [tex]\( 42.11\% \)[/tex], not [tex]\( 93.8\% \)[/tex].
