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Solution 11:
First term \( a = 3 \), common difference \( d = 4 \), number of terms \( n = 15 \).
Sum of an arithmetic sequence:
S_n = \frac{n}{2} \left(2a + (n-1)d\right)
S_{15} = \frac{15}{2} \left(2 \times 3 + 14 \times 4\right) = \frac{15}{2} \times (6 + 56) = \frac{15}{2} \times 62 = 15 \times 31 = 465
#### #### 465
Question 12:
The probability of event \( A \) is 0.4, and the probability of event \( B \) is 0.5. If \( A \) and \( B \) are independent, what is the probability of both \( A \) and \( B \) occurring?
Solution 12:
Since \( A \) and \( B \) are independent: