Question

Find P (Freshman(Girl) Hint: P(A and B)

P(B)
Classroom of Students
Boys Girls
Freshman 4 4 8
Sophomore 5 7 12
Junior 2 3 5
Senior 1
4 5
12 18
Reduce your fraction to lowest terms.
Enter the number that belongs in the green box.

Answer 1

`\sf \frac29`

Explanation:

From the table:

• Total number of Girls = 18

• Total number of students = 30

• Total number of Girls who are Freshman = 4

`\sf Probability \ of \ an \ event \ occurring = (Number \ of \ ways \ it \ can \ occur)/(Total \ number \ of \ possible \ outcomes)`

`\sf \implies P(Girl)=(18)/(30)`

`\sf \implies P(Freshman \cap Girl)=(4)/(30)`

`\begin{aligned}\sf P(Freshman|Girl)& = \sf(P(Freshman \cap Girl))/(P(Girl))\\\\ & = \sf (4)/(30) / (18)/(30)\\\\ & \sf=(4)/(30) * (30)/(18)\\\\ & = \sf \frac29\end{aligned}`