Answered

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Question 7 (5 points)

Suppose that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent events, [tex]\( P(A) = 0.93 \)[/tex] and [tex]\( P(B) = 0.41 \)[/tex]. Find [tex]\( P(A \text{ and } B) \)[/tex].

A. [tex]\( 1.34 \)[/tex]
B. [tex]\( 0.3813 \)[/tex]
C. [tex]\( 0.52 \)[/tex]
D. [tex]\( 0.41 \)[/tex]

Sagot :

GinnyAnswer
To determine the joint probability [tex]\( P(A \text{ and } B) \)[/tex] for two independent events [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we use the rule that states:

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

Given the probabilities:
- [tex]\( P(A) = 0.93 \)[/tex]
- [tex]\( P(B) = 0.41 \)[/tex]

By applying the formula for independent events:

[tex]\[ P(A \text{ and } B) = 0.93 \times 0.41 \][/tex]

The result of this multiplication is:

[tex]\[ P(A \text{ and } B) = 0.3813 \][/tex]

Therefore, the correct answer is:

[tex]\[ \boxed{0.3813} \][/tex]

So, the answer is [tex]\( \text{b) 0.3813} \)[/tex].
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