Question

Suppose P(C) = .2, P(M ⋂ C) = .07, and P(M ⋃ C) = .53. Find the indicated probability.2) P[(M)']

Answer 1

In order to find P[(M)'], we first need to find P(M). We can find it using the following formula:

$P(M\cup C)=P(M)+P(C)-P(M\cap C)$

Using the values provided, we have that:

$\begin{gathered} 0.53=P(M)+0.2-0.07 \\ P(M)=0.53-0.2+0.07 \\ P(M)=0.4 \end{gathered}$

Now, using the formula for complementary events, we have:

$\begin{gathered} P(M)+P(M^{\prime})=1 \\ 0.4+P(M^{\prime})=1 \\ P(M^{\prime})=1-0.4 \\ P(M^{\prime})=0.6 \end{gathered}$

So we have that P[(M)'] = 0.6