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Given:
[tex]\[ P(A) = 0.50, \ P(B) = 0.30, \ \text{and} \ P(A \ \text{and} \ B) = 0.15 \][/tex]

What is [tex]\[ P(A \ \text{or} \ B) \][/tex]?

A. 0.18

B. 0.65

C. 0.20

D. 0.80

Sagot :

GinnyAnsweridn
To find [tex]\( P(A \text{ or } B) \)[/tex], we use the formula for the union of two events in probability. The formula is:

[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]

where:
- [tex]\( P(A) \)[/tex] is the probability of event A occurring.
- [tex]\( P(B) \)[/tex] is the probability of event B occurring.
- [tex]\( P(A \text{ and } B) \)[/tex] is the probability of both events A and B occurring simultaneously.

Given:
- [tex]\( P(A) = 0.50 \)[/tex]
- [tex]\( P(B) = 0.30 \)[/tex]
- [tex]\( P(A \text{ and } B) = 0.15 \)[/tex]

We substitute these values into the formula:

[tex]\[ P(A \text{ or } B) = 0.50 + 0.30 - 0.15 \][/tex]

Now, we perform the arithmetic step-by-step:

1. Add [tex]\( P(A) \)[/tex] and [tex]\( P(B) \)[/tex]:
[tex]\[ 0.50 + 0.30 = 0.80 \][/tex]

2. Subtract [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\[ 0.80 - 0.15 = 0.65 \][/tex]

Therefore, the probability of either event A or event B occurring is [tex]\( P(A \text{ or } B) = 0.65 \)[/tex].

So, the correct answer is:
B. 0.65
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