Question

[50 points!]

Answer 1

Answer:

$\sf \dfrac13$

Step-by-step explanation:

From the table:

• Total number of Boys = 12
• Total number of students = 30
• Total number of Boys who are Freshman = 4

$\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}$

$\sf \implies P(Boy)=\dfrac{12}{30}$

$\sf \implies P(Freshman \cap Boy)=\dfrac{4}{30}$

$\begin{aligned}\sf P(Freshman|Boy) & = \sf\dfrac{P(Freshman \cap Boy)}{P(Boy)}\\\\ & = \sf\dfrac{4}{30} \div \dfrac{12}{30}\\\\ & = \sf\dfrac{4}{30}\times \dfrac{30}{12}\\\\ & = \sf \dfrac{4}{12}\\\\ & = \sf\dfrac{1}{3}\end{aligned}$

Answer 2

Answer:

1/3

Explanation:

P(Freshman | Boy)

• Freshman = 4

• Boy = 12

⇒ Probability = Number of favorable outcomes ÷ Total number of possible outcomes

• P(Freshman | Boy) = freshman/total boys

• P(Freshman | Boy) = 4/12

• P(Freshman | Boy) = 1/3