Question

[50 points]

P(AB) = P(An B)/P(B)

Freshmen
Sophomores
Juniors
Seniors
Boys
3
1
4
2
Girls
7
9
5
1
P(Boy|Sophomore) =

Answer 1

1/10

Step-by-step explanation:

Given Boy Sophomores: 1

Given Total Boy: 3 + 1 + 4 + 2 = 10

So

⇒ P(Boy|Sophomore)

⇒ Boy Sophomore/Total Boy

⇒ 1/10

Answer 2

`\sf (1)/(10)`

Step-by-step explanation:

From the table:

• Total number of Sophomores = 10
• Total number of students = 37
• Total number of Boys who are Sophomores = 1

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

`\sf \implies P(Sophomore)=(10)/(37)`

`\sf \implies P(Boy \cap Sophomore)=(1)/(37)`

`\begin{aligned}\sf P(Boy | Sophomore) & = \sf(P(Boy \cap Sophomore))/(P(Sophomore))\\\\ & = \sf (1)/(37) / (10)/(37)\\\\ & = \sf(1)/(37) *(37)/(10)\\\\ & = \sf(1)/(10)\end{aligned}`