Question

Given events J and K: P(J) = 0.18; P(K) = 0.37; P(J OR K) = 0.45

a. Find P(J AND K).

b. Find the probability of the complement of event (J AND K).

c. Find the probability of the complement of event (J OR K).

Short answer

a.$P(JANDK)=0.10$

b.$P\left(\right(JANDK)\text{'})=0.90$

c.$P\left(\right(JORK)\text{'})=0.55$

Step-by-step solution

Given information

Given events J and K: P(J) = 0.18; P(K) = 0.37; P(J OR K) = 0.45

Explanation (part a)

we know that

$P(JORK)=P\left(J\right)+P\left(K\right)-P(JANDK)$

On rearranging,

$P(JANDK)=P\left(J\right)+P\left(K\right)-P(JORK)$

Plugging the given values, we get

localid="1650389819200" $$\begin{gathered} P(JANDK)=0.18+0.37-0.45 \\ P(JANDK)=0.10 \end{gathered}$$

Explanation (part b)

the probability of the complement of event (J AND K):

$$\begin{gathered} P\left(\right(JANDK)\text{'})=1-P(JANDK) \\ P\left(\right(JANDK)\text{'})=1-0.10 \\ P\left(\right(JANDK)\text{'})=0.90 \end{gathered}$$

Explanation (part c)

the probability of the complement of event (J OR K):

$$\begin{gathered} P\left(\right(JORK)\text{'})=1-P(JORK) \\ P\left(\right(JORK)\text{'})=1-0.45 \\ P\left(\right(JORK)\text{'})=0.55 \end{gathered}$$