Problem: Ms. Ashol has 20 boys and 16 girls in her mathematics class. If she chooses two students at random to work on the blackboard, what is the probability that both students chosen are girls?
What I did : I added the boys and girls 36
(16c2)/(36c16)
Yes 36
first girl
16/36
second girl
15/35
so
16/36 * 15/35
I’m confused why it was 15/36 for the second girl though wouldn’t it be 15/35
Yes, I said
first 16/36
second 15/35
To find the probability that both students chosen are girls, we need to determine the total number of possible outcomes (the sample space) and the number of favorable outcomes (the desired outcome where both students chosen are girls).
Step 1: Determine the total number of possible outcomes (sample space):
The total number of students in the class is 20 boys + 16 girls = 36 students.
Step 2: Determine the number of favorable outcomes (both students chosen are girls):
The number of ways to choose 2 students from the 16 girls is represented by the combination "16 choose 2" or "16C2." This can be calculated as follows:
16C2 = (16!)/(2!(16-2)!) = (16!) / (2!14!) = (16 * 15) / (2 * 1) = 120.
Step 3: Calculate the probability:
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes.
Therefore, the probability that both students chosen are girls is:
Probability = 120 / (36C2).
Note: (36C2) represents the number of ways to choose 2 students from the total 36 students in the class and can be calculated as follows:
36C2 = (36!)/(2!(36-2)!) = (36!) / (2!34!) = (36 * 35) / (2 * 1) = 630.
Substituting the values:
Probability = 120 / 630 = 0.1905.
Thus, the probability that both students chosen are girls is approximately 0.1905 or 19.05%.