section 5.2 homework\nscore: 2/15 answered: 2/15\nquestion 3\nfind the indicated probability\ngiven\np(a) =…
section 5.2 homework\nscore: 2/15 answered: 2/15\nquestion 3\nfind the indicated probability\ngiven\np(a) = 0.3\np(b) = 0.3\np(a or b) = 0.42\nfind\np(a and b) =\nare these events disjoint?\nyes\nno
Answer
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 $P(A\ and\ B)=0.18\neq0$, the events are not disjoint.
Answer:
$P(A\ and\ B)=0.18$ No