Question

find the indicated probability
given
p(a) = 0.4
p(b) = 0.2
p(a or b) = 0.6
find
p(a and b) =
are these events disjoint?
yes
no

Explanation:

Step1: Recall the addition - rule formula

The formula for $P(A\ or\ B)$ is $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$.

Step2: Rearrange the formula to solve for $P(A\ and\ B)$

We can rewrite the formula as $P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)$.

Step3: Substitute the given values

Substitute $P(A) = 0.4$, $P(B)=0.2$ and $P(A\ or\ B)=0.6$ into the formula. So, $P(A\ and\ B)=0.4 + 0.2-0.6$.

Step4: Calculate the value of $P(A\ and\ B)$

$P(A\ and\ B)=0$.

Step5: Determine if the events are disjoint

Two events $A$ and $B$ are disjoint if $P(A\ and\ B) = 0$. Since $P(A\ and\ B)=0$, the events are disjoint.

Answer:

$P(A\ and\ B)=0$
Yes