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[tex]$A$[/tex] and [tex]$B$[/tex] are independent events. [tex]$P(A) = 0.50$[/tex] and [tex]$P(B) = 0.20$[/tex]. What is [tex]$P(A \text{ and } B)$[/tex]?

A. 0
B. 0.01
C. 0.70
D. 0.10

Sagot :

GinnyAnswer
To find the probability of two independent events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring together, we use the formula:

[tex]\[ P(A \text{ and } B) = P(A) \times P(B) \][/tex]

We know from the problem statement that:
[tex]\[ P(A) = 0.50 \][/tex]
[tex]\[ P(B) = 0.20 \][/tex]

Now, we need to multiply these probabilities together:

[tex]\[ P(A \text{ and } B) = 0.50 \times 0.20 \][/tex]

By performing the multiplication, we get:

[tex]\[ P(A \text{ and } B) = 0.10 \][/tex]

So, the probability of both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occurring together is:

[tex]\[ P(A \text{ and } B) = 0.10 \][/tex]

Thus, the correct answer is:

D. 0.10
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