Mrs. /green is randomly choosing team captains from her class of 12 girls and 10 boys. ?She draw one name from the bag, SETS IT ASIDE, and then chooses a second name. /What is the probability that both team captains are girls? I would say it is 2/7 Can someone check to see if this is right? Please
Probability that a girl is picked from 22 people:
12/22
Probability that another girl is picked from 21 people:
11/21
Probability that both occur:
(12/22) x (11/21) = 132/462 = 2/7
so, yes, you are correct
To find the probability that both team captains are girls, we need to first determine the total number of possible outcomes and the number of favorable outcomes.
There are a total of 22 students in the class (12 girls and 10 boys).
When Mrs. Green draws the first name and sets it aside, there are now 21 students left in the bag. Out of these, 11 are girls and 10 are boys.
To calculate the probability of the first name being a girl, we divide the number of favorable outcomes (12 girls) by the total number of possible outcomes (22 students):
P(First name is a girl) = 12/22
After removing one girl from the bag, there are now 21 students left, with 11 girls and 10 boys.
To calculate the probability of the second name being a girl, we divide the number of favorable outcomes (11 girls) by the total number of possible outcomes (21 students):
P(Second name is a girl) = 11/21
To find the probability that both team captains are girls, we multiply the probabilities of each event:
P(Both team captains are girls) = P(First name is a girl) * P(Second name is a girl)
P(Both team captains are girls) = (12/22) * (11/21)
Simplifying the expression:
P(Both team captains are girls) = 2/7
So, the correct answer is indeed 2/7.