Question

a lottery game has balls numbered 1 through 15. what is the probability of selecting an even numbered ball or the number 12 ball?
a. $\frac{5}{4}$
c. $\frac{4}{5}$
b. 7
d. $\frac{7}{15}$
please select the best answer from the choices provided
○ a
○ b
○ c
○ d

Explanation:

Step1: Determine the number of even - numbered balls

The even - numbered balls from 1 to 15 are 2, 4, 6, 8, 10, 12, 14. So \(n(\text{even}) = 7\).

Step2: Use the formula for the probability of the union of two events

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event of selecting an even - numbered ball and \(B\) be the event of selecting the ball numbered 12.
The probability of an event \(E\) is \(P(E)=\frac{n(E)}{n(S)}\), where \(n(S) = 15\) (total number of balls).
\(P(A)=\frac{7}{15}\), \(P(B)=\frac{1}{15}\), and \(P(A\cap B)=\frac{1}{15}\) (since 12 is already counted in the even - numbered balls).
Then \(P(A\cup B)=\frac{7 + 1-1}{15}\).

Answer:

D. \(\frac{7}{15}\)