Question

CONDITIONAL PROBABILITY ASSISTANCE

Answer 1

Consider such events:

A - selected student is freshmen

B - selected student is girl

`A\cap B` - selected student is freshman is girl

`A|B` - choosen girl is freshmen.

Use formula
`Pr(A|B)=(Pr(A\cap B))/(Pr(B))`.

From the table you can see that girls that are freshmen are 4 from all 30 people, then
`Pr(A\cap B)=(4)/(30)`. There are 18 girls, then
`Pr(B)=(18)/(30)`. Substitute into the formula:

`Pr(A|B)=((4)/(30) )/((18)/(30) )=(4)/(18) =(2)/(9)`.

Answer:
`Pr(A|B)=(2)/(9)`.