Question

Conditional Probability Worksheet -1002Given the following information: P(D) = 0.7, P(E) = 0.2, and P(D and E) = 0.15.1. Find the P(DIE)log2. Find the P(ED)onded(31)Saulno) Banosvd bomvog(TASalich classes.

Answer 1

Formula:

$P(A\cap B)=P(B)\cdot P(A|B)$

Given:

P(D)=0.7

P(E)=0.2

P(D and E)=0.15

$\begin{gathered} P(D\cap E)=0.15 \\ \end{gathered}$

Formula :

$\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ \end{gathered}$

Then:

$\begin{gathered} P(D\cap E)=P(E)\cdot P(D|E) \\ P(D|E)=\frac{0.15}{0.2} \\ =0.75 \end{gathered}$

(B)

$\begin{gathered} P(D|E)+P(E|D)=1 \\ 0.75+P(E|D)=1 \\ P(E|D)=1-0.75 \\ =0.25 \end{gathered}$