QuestionFind $P(A$ OR $B)$ given $P(A)=0.7$ , $P(B)=0.2$ , and $P(A$ AND $B)=0.17$ .

Studdy Solution

STEP 1

Assumptions1. $A$ and $B$ are events in a probability space. . The probability of event $A$ occurring, denoted $(A)$ , is0.7.
3. The probability of event $B$ occurring, denoted $(B)$ , is0..
4. The probability of both events $A$ and $B$ occurring, denoted $(A \text{ AND } B)$ , is0.17.
5. We are asked to find the probability of either event $A$ or event $B$ occurring, denoted $(A \text{ OR } B)$ .

STEP 2

We use the formula for the probability of the union of two events, which is given by $(A \text{ OR } B) =(A) +(B) -(A \text{ AND } B)$

STEP 3

Now, plug in the given values for $(A)$ , $(B)$ , and $(A \text{ AND } B)$ to calculate $(A \text{ OR } B)$ .
$(A \text{ OR } B) =0.7 +0.2 -0.17$

STEP 4

Calculate the value of $(A \text{ OR } B)$ .
$(A \text{ OR } B) =0.7 +0.2 -0.17 =0.73$ So, the probability of either event $A$ or event $B$ occurring is0.73.

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