Mrs. Baker has to choose 2 students to lead the class field trip. If she draws from a list of 6 boys and 6 girls, what is the probability that 2 girls will be drawn?
(Please Help!)
A.1/7
B.5/24
C.5/22
D.5/6
To find the probability of drawing 2 girls out of a total of 6 boys and 6 girls, we need to calculate the number of favorable outcomes (drawing 2 girls) and divide it by the total number of possible outcomes (drawing 2 students from a list of 12).
First, let's find the number of ways to choose 2 girls out of 6. This can be calculated using the combination formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of options and r is the number of options to be chosen.
Using this formula, we have C(6, 2) = 6! / (2!(6 - 2)!) = 6! / (2!4!) = (6 * 5 * 4!) / (2!4!) = (6 * 5) / 2! = 30 / 2 = 15.
So, there are 15 ways to choose 2 girls out of a total of 6 girls.
Next, let's find the number of possible outcomes when choosing 2 students out of 12 (6 boys + 6 girls). This can be calculated using the combination formula as well: C(12, 2) = 12! / (2!(12 - 2)!) = 12! / (2!10!) = (12 * 11) / 2 = 132.
Therefore, the probability of drawing 2 girls is the number of favorable outcomes divided by the total number of outcomes, which is 15/132.
Simplifying this fraction, we get 5/44.
Therefore, the correct answer is option C. 5/22.
Hope this explanation helps!
Pr= 6/12*5/11= ?
Any 2 of 12 is (12 x 11)/2 = 66. Any 2 from 6 is (6 x 5)/2 = 15 so the probability is 15 out of 66 ie 0.227 or 22.7%
Loui