Question

Suppose p(x1) = .75 and p(y2 | x1) = .40. what is the joint probability of x1 and y2?

Answer 1

By definition of conditional probability,

$\mathbb P(Y_2\mid X_1)=\dfrac{\mathbb P(Y_2\cap X_1)}{\mathbb P(X_1)}$

so

$\mathbb P(Y_2\cap X_1)=0.40\times0.75=0.3$

Answer 2

The joint probability of x1 and y2 is  P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.

What is the probability about?

In the joint probability of x1 and y2 is  P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).

Therefore:

P(Y₂ ∩ X₁ )

=0.40 x 0.75

= 0.3

Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is  P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.

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