Question

In a class with $\frac{3}{5}$ women and $\frac{2}{5}$ men, $25\%$ of the women are business majors. Find the probability that a student chosen from the class at random is a female business major.

• A. 0.6
• B. 0.15
• C. 0.13
• D. 0.14

Answer 1

The correct option is B

0.15

W=the student is a woman

B= the student is a business major "class with $\frac{3}{5}$ women" $\Rightarrow P\left(W\right)=\frac{3}{5}=0.60$

"$25\%$ of the women are business majors" is the same as saying "the probabilty a stuent is a business major,given the student is a woman is 0.25"

$\Rightarrow P\left(B|W\right)=0.25$"probability that a student chosen from the class at random is a female business major" is the same as saying "probability student is a woman and a business major" $\Rightarrow P\left(WandB\right)$

Use the multiplication rule to answer the question:

$P\left(WandB\right)=P\left(W\right).P\left(B|W\right)=\left(0.60\right)\left(0.25\right)=0.15$