Question

Question: Given P(X) = 0.5, P(Y) = 0.4, and P(Y|X) = 0.3, what are P(X and Y) and P(X or Y)? (3 points)

A. P(X and Y) = 0.9, P(X or Y) = 0.75
B. P(X and Y) = 0.9, P(X or Y) = 0.1
C. P(X and Y) = 0.75, P(X or Y) = 0.15
D. P(X and Y) = 0.15, P(X or Y) = 0.1
E. P(X and Y) = 0.15, P(X or Y) = 0.75

Answer 1

`P(x\ and\ y) = 0.15`

`P(x\ or\ y) = 0.75`

Step-by-step explanation:

Given

`P(x) = 0.5`

`P(y) = 0.4`

`P(y|x) = 0.3`

Solving (a):
`P(x\ and\ y)`

In probability, this is calculated as:

`P(x\ and\ y) = P(x) * P(y|x)`

This gives:

`P(x\ and\ y) = 0.5 * 0.3`

`P(x\ and\ y) = 0.15`

Solving (b):
`P(x\ or\ y)`

In probability, this is calculated as:

`P(x\ or\ y) = P(x) + P(y) - P(x\ and\ y)`

This gives:

`P(x\ or\ y) = 0.5 + 0.4 - 0.15`

`P(x\ or\ y) = 0.75`