Question

Given P(X) = 0.6, P(Y) = 0.3, and P(Y|X) = 0.05, what are P(X and Y) and P(X or Y)?

Group of answer choices
A. P(X and Y) = 0.03, P(X or Y) = 0.87
B. P(X and Y) = 0.03, P(X or Y) = 0.35
C. P(X and Y) = 0.9, P(X or Y) = 0.87
D. P(X and Y) = 0.9, P(X or Y) = 0.35
Please help it I'd appreciate it alot

Answer 1

`P(X\cap Y)=0.03\\ \\P(X\cup Y)=0.87`

Explanation:

1. Use formula

`P(Y|X)=(P(X\cap Y))/(P(X))`

So,

`0.05=(P(X\cap Y))/(0.6)\Rightarrow P(X\cap Y)=0.05\cdot 0.6=0.03`

2. Use formula:

`P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)`

So,

`P(X\cup Y)=0.6+0.3-0.03=0.9-0.03=0.87`