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Question 1 of 10

Suppose [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent events. If [tex]\(P(A) = 0.7\)[/tex] and [tex]\(P(B) = 0.8\)[/tex], what is [tex]\(P(A \cap B)\)[/tex]?

A. 0.7
B. 0.8
C. 0.15
D. 0.56

Sagot :

GinnyAnsweridn
To find the probability of both independent events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occurring, denoted as [tex]\( P(A \cap B) \)[/tex], we use the rule for the probability of the intersection of two independent events. This rule states that for two independent events [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:

[tex]\[ P(A \cap B) = P(A) \times P(B) \][/tex]

Given the probabilities:
[tex]\[ P(A) = 0.7 \][/tex]
[tex]\[ P(B) = 0.8 \][/tex]

We multiply these probabilities together:
[tex]\[ P(A \cap B) = 0.7 \times 0.8 \][/tex]

Carrying out the multiplication:
[tex]\[ 0.7 \times 0.8 = 0.56 \][/tex]

Therefore, the probability that both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occur is:

[tex]\[ P(A \cap B) = 0.56 \][/tex]

So, the correct answer is:
D. 0.56
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