A school club consists of 22 male students and 15 female students. If 3 students are selected to represent the club in the student government, what is the probability 2 will be male and 1 will be female?
prob(your event)
= C(22,2)*C(15,1)/C(37,3)
= 33/74
To calculate the probability of selecting 2 male students and 1 female student from the club, we need to find the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes can be calculated by selecting 3 students from a total of 37 students (22 males + 15 females) which can be denoted as 37C3 (combination formula).
The number of favorable outcomes can be calculated by selecting 2 male students from 22 male students (22C2) and selecting 1 female student from 15 female students (15C1). We multiply these two numbers to find the total number of favorable outcomes.
Now let's calculate the probability step-by-step.
Step 1: Calculate the total number of outcomes.
The total number of outcomes = 37C3 = (37!)/(3!(37-3)!) = (37!)/(3!34!)
Step 2: Calculate the number of favorable outcomes.
The number of favorable outcomes (selecting 2 males from 22 males and 1 female from 15 females) = (22C2) * (15C1) = [(22!)/(2!(22-2))] * (15!/(1!(15-1)!))
= (22!)/(2!20!) * (15!)/(1!14!)
Step 3: Calculate the probability.
The probability = Number of favorable outcomes/ Total number of outcomes
= [(22!)/(2!20!)] * [(15!)/(1!14!)] / [(37!)/(3!34!)]
= (22 * 21 * 15) / (37 * 36 * 35)
= 0.222 (rounded to three decimal places)
Therefore, the probability of selecting 2 male students and 1 female student is 0.222 or 22.2%.
To find the probability, first, we need to determine the total number of ways we can select 3 students from the club. We will use the combination formula, also known as "n choose k".
The total number of ways to choose 3 students from a club of 37 (22 males + 15 females) can be calculated as:
C(37, 3) = 37! / (3!(37-3)!) = 37! / (3!34!) = (37*36*35) / (3*2*1) = 7770.
Now, we need to determine the number of ways to choose 2 males out of 22 and 1 female out of 15. We will use the same combination formula for both cases.
Number of ways to choose 2 males out of 22:
C(22, 2) = 22! / (2!(22-2)!) = 22! / (2!20!) = (22*21) / (2*1) = 231.
Number of ways to choose 1 female out of 15:
C(15, 1) = 15! / (1!(15-1)!) = 15! / (1!14!) = 15.
To find the probability of selecting 2 males and 1 female, we multiply the number of ways to choose 2 males and 1 female by the probabilities of each individual event and divide by the total number of ways to choose 3 students:
Probability = (number of ways to choose 2 males * number of ways to choose 1 female) / total number of ways to choose 3 students
= (231 * 15) / 7770
= 1155 / 7770
≈ 0.1487.
Therefore, the probability that 2 students will be male and 1 student will be female is approximately 0.1487, or 14.87%.