To solve for the probability of both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] happening, given that they are independent, we can follow these steps:
1. Understand the Concept of Independent Events:
Independent events are events where the occurrence of one event does not affect the probability of the other event occurring. For such events, the probability of both events occurring together is the product of their individual probabilities.
2. Identify the Given Probabilities:
- [tex]\( P(A) \)[/tex] is the probability of event [tex]\( A \)[/tex] occurring, which is [tex]\( 0.93 \)[/tex].
- [tex]\( P(B) \)[/tex] is the probability of event [tex]\( B \)[/tex] occurring, which is [tex]\( 0.41 \)[/tex].
3. Calculate [tex]\( P(A \text{ and } B) \)[/tex]:
- Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are independent, the formula for the probability of both events occurring [tex]\( P(A \text{ and } B) \)[/tex] is:
[tex]\[
P(A \text{ and } B) = P(A) \times P(B)
\][/tex]
4. Substitute the Given Probabilities into the Formula:
[tex]\[
P(A \text{ and } B) = 0.93 \times 0.41
\][/tex]
5. Multiply the Probabilities:
[tex]\[
0.93 \times 0.41 = 0.3813
\][/tex]
6. Conclusion:
Therefore, the probability of both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occurring is [tex]\( 0.3813 \)[/tex].
Based on the available options:
○ a 1.34
○ b 0.3813
○ c 0.52
○ d 0.41
The correct answer is:
○ b 0.3813
