Question

[50 points!]

Find P (Freshman | Boy)

Hint:
P(A and B)/P(B)

Classroom of Students:
Boys Girls
Freshman 4 4 8
Sophomore 57 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 \frac13`

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 = (Number \ of \ ways \ it \ can \ occur)/(Total \ number \ of \ possible \ outcomes)`

`\sf \implies P(Boy)=(12)/(30)`

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

`\begin{aligned}\sf P(Freshman|Boy) & = \sf(P(Freshman \cap Boy))/(P(Boy))\\\\ & = \sf(4)/(30) / (12)/(30)\\\\ & = \sf(4)/(30)* (30)/(12)\\\\ & = \sf (4)/(12)\\\\ & = \sf(1)/(3)\end{aligned}`

Answer 2

1/3

Step-by-step 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