Question

There are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. If the selection is random, what is the probability of selecting a team of 4 girls and 6 boys?

Answer 1

The probability of selecting a team of 4 girls and 6 boys randomly from a class of 6 girls and 7 boys using the hypergeometric distribution is approximately 0.3669.

Step-by-step explanation:

To calculate the probability of selecting a team of 4 girls and 6 boys from a class with 6 girls and 7 boys, we use the hypergeometric distribution, as this is a problem of sampling without replacement from two distinct groups.

The total number of ways to select a team of 10 players from the 13 students (6 girls + 7 boys) is:

Total combinations = C(13, 10) = 13! / (10! * 3!) = 286 ways

The number of ways to choose exactly 4 girls from the 6 available is:

Combinations of girls = C(6, 4) = 6! / (4! * 2!) = 15 ways

The number of ways to choose exactly 6 boys from the 7 available is:

Combinations of boys = C(7, 6) = 7! / (6! * 1!) = 7 ways

So, the probability of choosing a team of 4 girls and 6 boys is calculated as the number of favorable combinations divided by the total number of combinations:

Probability = (Combinations of girls * Combinations of boys) / Total combinations

Probability = (15 * 7) / 286

Probability = 105 / 286

Probability ≈ 0.3669

Answer 2

For the selection to be 10, there has to be at least 3 girls. So there's a 1/4 chance of 3 girls picked, 1/4 4 girls, 1/4 5 girls and 1/4 6 girls. Because the sum of people has to be 10, if 4 girls are picked, to make 10 people there is a 1/1 chance of 6 boys. 1/4 * 1/1 = 1/4. So 1/4 chance of 4 girls and 6 boys