To find the probability that a female is elected president and a male is elected vice president, follow these steps:
1. Determine the total number of candidates:
There are 4 females and 3 males, so the total number of candidates is:
[tex]\[
4 + 3 = 7
\][/tex]
2. Calculate the probability that a female is elected president:
The number of females is 4 out of a total of 7 candidates. So the probability that a female is elected president is:
[tex]\[
\frac{4}{7}
\][/tex]
3. Determine the new number of remaining candidates after a female is elected president:
After a female is elected president, 6 candidates remain (3 males and 3 females).
4. Calculate the probability that a male is elected vice president given a female is already elected president:
The number of males is 3 out of the remaining 6 candidates. So the probability that a male is elected vice president given that a female is already president is:
[tex]\[
\frac{3}{6} = \frac{1}{2}
\][/tex]
5. Find the combined probability:
Multiply the probability of each event to find the combined probability that both a female is elected president and a male is elected vice president. Thus,
[tex]\[
\frac{4}{7} \times \frac{1}{2} = \frac{4 \times 1}{7 \times 2} = \frac{4}{14} = \frac{2}{7}
\][/tex]
Therefore, the probability that a female is elected president and a male is elected vice president is [tex]\(\frac{2}{7}\)[/tex].
The correct answer is:
C. [tex]\(\frac{2}{7}\)[/tex]
