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

Answer:

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

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

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:

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

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