Question

favorite ice cream flavor
chocolate\tstrawberry\tvanilla\ttotal
gender\tmale\t22\t17\t15\t54
\tfemale\t15\t16\t4\t35
\ttotal\t37\t33\t19\t89
in 1-3, use the two way table above.

1. find the probability of choosing a student that is male and prefers vanilla ice cream.

$p(m cap v) = \frac{15}{89} \approx 0.17$

1. find the probability of a randomly selected student choosing chocolate.

$p(c) = \frac{37}{89} \approx 0.42$

1. hershey’s factory wants to film a commercial with real students. they are going to ask random students which is their favorite flavor of ice cream with the hope that the student will claim that chocolate is their favorite flavor. to help hersey’s with their goal, you are going to restrict the commercial to either all males or all females. which group should you pick? explain your answer and support it mathematically.

females are more likely to

Explanation:

Step1: Calculate male chocolate prob

$P(\text{Chocolate}|\text{Male}) = \frac{22}{54} \approx 0.407$

Step2: Calculate female chocolate prob

$P(\text{Chocolate}|\text{Female}) = \frac{15}{35} \approx 0.429$

Step3: Compare the two probabilities

$0.429 > 0.407$

Answer:

You should pick the female group. The probability that a female student prefers chocolate is $\frac{15}{35} \approx 0.429$, while the probability that a male student prefers chocolate is $\frac{22}{54} \approx 0.407$. Since the probability is higher for female students, this group is more likely to have a student who prefers chocolate, which aligns with Hershey's goal.