A STUDENT COUNCIL COMMITTEE IS MADE UP OF 4 BOYS AND 5 GIRLS.IF 2 COMMITTEE MEMBERS ARE CHOSEN AT RANDOM TO ATTEND A CONFERENCE,WHAT IS THE PROBABILITY THAT BOTH MEMBERS WILL BE BOYS?
probability of first boy = 4/9
probability of second boy = 3/8
so
4/9 * 3/8 = 3/18 = 1/6
What’s the answer
To find the probability that both members chosen will be boys, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
From a committee of 4 boys and 5 girls, a total of 9 committee members can be chosen to attend the conference. When selecting 2 members, we have to consider the possible combinations or pairs of committee members that can be chosen. This can be calculated using the combination formula, which is given by:
nCr = n! / (r!(n-r)!)
where n is the total number of objects to choose from, and r is the number of objects to be chosen.
In this case, we have:
n = 9 (total committee members)
r = 2 (committee members to be chosen)
Applying the combination formula:
9C2 = 9! / (2!(9-2)!)
= (9 x 8 x 7!) / (2 x 1 x 7!)
= (9 x 8) / (2 x 1)
= 36
Therefore, there are a total of 36 possible outcomes when choosing 2 committee members from the student council committee.
Number of favorable outcomes:
Since we want both selected members to be boys, we need to consider the possible combinations of selecting 2 boys from the 4 available.
Using the combination formula again:
4C2 = 4! / (2!(4-2)!)
= (4 x 3 x 2!) / (2 x 1 x 2!)
= 6
Therefore, there are 6 ways to select 2 boys from the 4 available.
Probability calculation:
Finally, we can find the probability that both members selected will be boys by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 36
= 1 / 6
So, the probability that both members chosen to attend the conference will be boys is 1/6 or approximately 0.167.