Question

section 5.2 homework
score: 4/15 answered: 4/15
question 5
find the indicated probability
given
p(a) = 0.5
p(a or b) = 0.7
p(a and b) = 0.2
find
p(b) =
are these events disjoint?
yes
no

Explanation:

Step1: Recall the formula for P(A or B)

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Step2: Rearrange the formula to solve for P(B)

$P(B)=P(A\cup B)+P(A\cap B)-P(A)$

Step3: Substitute the given values

$P(B)=0.7 + 0.2-0.5$
$P(B)=0.4$

Step4: Determine if events are disjoint

Disjoint events have $P(A\cap B) = 0$. Since $P(A\cap B)=0.2
eq0$, the events are not disjoint.

Answer:

$P(B)=0.4$
No