Home > AI > Math > Probability > Conditional Probability >

3929

Conditional Probability shark 1 min read

Q: What’s the expected value of a d6, given that the outcome is prime?

(1)   \begin{align*}P(p) & = \frac{3}{6} = \frac{1}{2} \\P( 1 | p) & = \frac{P(1 \cap p)}{P(p)} = \frac{0}{\frac{1}{2}} = 0 \\P( 2 | p) & = \frac{P(2 \cap p)}{P(p)} \\& = \frac{\frac{1}{6}}{\frac{1}{2}} = \frac{1}{3} \\P( 3 | p) & = \frac{P(3 \cap p)}{P(p)} \\& = \frac{\frac{1}{6}}{\frac{1}{2}} = \frac{1}{3} \\P( 5 | p) & = \frac{P(5 \cap p)}{P(p)} \\& = \frac{\frac{1}{6}}{\frac{1}{2}} = \frac{1}{3} \\E(X) = \frac{1}{3} \times(2+3+5) = \frac{10}{3}\end{align*}


Share this post:
Related posts:

Leave a Reply