Question

section 5.2 homework
score: 2/15 answered: 2/15
question 3
find the indicated probability
given
p(a) = 0.3
p(b) = 0.3
p(a or b) = 0.42
find
p(a and b) =
are these events disjoint?
yes
no

Explanation:

Step1: Recall probability formula

Use the formula $P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$.

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

$P(A\ and\ B)=P(A)+P(B)-P(A\ or\ B)$.

Step3: Substitute given values

$P(A\ and\ B)=0.3 + 0.3-0.42$.
$P(A\ and\ B)=0.18$.

Step4: Determine if events are disjoint

Disjoint events have $P(A\ and\ B) = 0$. Since $P(A\ and\ B)=0.18
eq0$, the events are not disjoint.

Answer:

$P(A\ and\ B)=0.18$
No