Question

A piece of legislation is judged to have a probability of 0.75 of passing the low house, 0.52 of passing the upper house, and 0.83 of passing the low house or the upper house. What is the probability to at it will pass both houses?

Answer 1

Given that;

`\begin{gathered} \text{Probability of passing low house=Pr(l)=0.75} \\ \text{Probability of passing upper house = Pr(U)=0.52} \\ \text{Probability of passing the low house or the upper house=}Pr(l\cup U)=0.83 \end{gathered}`

Therefore, we can find the probability that it will pass both houses using the formula below;

`\begin{gathered} Pr(L\cup U)=Pr(L)+Pr(U)-Pr(L\cap U) \\ \text{Where }Pr(L\cap U)=probability\text{ that it will pass both houses} \end{gathered}`

Thus;

`\begin{gathered} Pr(L\cup U)=Pr(L)+Pr(U)-Pr(L\cap U) \\ 0.83=0.75+0.52-Pr(L\cap U) \\ Pr(L\cap U)=1.24-0.83 \\ =0.41 \end{gathered}`

Therefore, the probability to at it will pass both houses is 0.41