Question

1. find the probability of the indicated event if p(e)=0.35 and p(f)=0.15 (a) (3pts) find p(e or f) if p(e and f) = 0.25 (b) (3pts) find p(e or f) if e and f are mutually exclusive. (c) (3pts) find p(e^c)

Explanation:

Step1: Recall the formula for P(E or F) with intersection

The formula for $P(E\cup F)$ is $P(E\cup F)=P(E)+P(F)-P(E\cap F)$. Given $P(E) = 0.35$, $P(F)=0.15$ and $P(E\cap F)=0.25$.
$P(E\cup F)=0.35 + 0.15-0.25$

Step2: Calculate the value for part (a)

$P(E\cup F)=0.35 + 0.15 - 0.25=0.25$

Step3: Recall the property for mutually - exclusive events

If E and F are mutually exclusive, then $P(E\cap F) = 0$. Using the formula $P(E\cup F)=P(E)+P(F)-P(E\cap F)$, we have $P(E\cup F)=P(E)+P(F)$.
$P(E\cup F)=0.35 + 0.15$

Step4: Calculate the value for part (b)

$P(E\cup F)=0.35+0.15 = 0.5$

Step5: Recall the formula for the complement of an event

The formula for the complement of an event E is $P(E^{c})=1 - P(E)$. Given $P(E)=0.35$.
$P(E^{c})=1 - 0.35$

Step6: Calculate the value for part (c)

$P(E^{c})=0.65$

Answer:

(a) $0.25$
(b) $0.5$
(c) $0.65$