Questions: A history class is comprised of 9 female and 5 male students. If the instructor of the class randomly chooses 12 students from the class for an oral exam, what is the probability that 8 female students and 4 male students will be selected? Round your answer to 3 decimal places. (If necessary, consult a list of formulas.)

A history class is comprised of 9 female and 5 male students. If the instructor of the class randomly chooses 12 students from the class for an oral exam, what is the probability that 8 female students and 4 male students will be selected? Round your answer to 3 decimal places. (If necessary, consult a list of formulas.)
Transcript text: A history class is comprised of 9 female and 5 male students. If the instructor of the class randomly chooses 12 students from the class for an oral exam, what is the probability that 8 female students and 4 male students will be selected? Round your answer to 3 decimal places. (If necessary, consult a list of formulas.)
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Solution

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Solution Steps

Step 1: Calculate Combinations for Females

To find the number of ways to choose 8 females from 9, use the combination formula:

\[ \binom{9}{8} = 9 \]

Step 2: Calculate Combinations for Males

To find the number of ways to choose 4 males from 5, use the combination formula:

\[ \binom{5}{4} = 5 \]

Step 3: Calculate Total Combinations

To find the total number of ways to choose 12 students from 14, use the combination formula:

\[ \binom{14}{12} = 91 \]

Step 4: Calculate Probability

The probability of selecting 8 females and 4 males is given by:

\[ \frac{\binom{9}{8} \times \binom{5}{4}}{\binom{14}{12}} = \frac{9 \times 5}{91} = 0.4945 \]

Final Answer

The probability that 8 female students and 4 male students will be selected is:

\[ \boxed{0.495} \]

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