Question

A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen top participate in the district debate. What is the probaility that 2 girland 2 boys will be selected?

Answer 1

The probability of selecting 2 girls and 2 boys from a debate team can be calculated using the hypergeometric distribution.

Step-by-step explanation:

The probability of selecting 2 girls and 2 boys from a debate team consisting of 4 girls and 6 boys can be calculated using the hypergeometric distribution. The group of interest is the boys and the sample is the 4 students being selected for the district debate.

1. Calculate the total number of ways to choose 4 students from the 10 students on the debate team: C(10, 4) = 210
2. Calculate the number of ways to choose 2 girls and 2 boys: C(4, 2) * C(6, 2) = 6 * 15 = 90
3. Calculate the probability: P(2 girls and 2 boys) = 90/210 = 9/21 = 3/7

Answer 2

The probability that 2 girls and 2 boys are selected is given by:

`P(\text{ 2 boys, 2 girls })=(4C2*6C2)/(10C4)=(6*15)/(210)=(3)/(7)`

Therefore, the correct choice is option D) 3/7.