FBM 124 class consists of 10 male and 12 female students. Two students were chosen to represent
the university to an international forum. Compute the probability of choosing
(a) two female students
(b) no more than 1 male student
c)same genders students
To compute the probabilities, we need to know the total number of students and the number of ways we can choose the students for each scenario.
(a) Let's calculate the probability of choosing two female students:
Total number of students = 10 (male) + 12 (female) = 22.
The number of ways to choose two female students out of 12 is given by the combination formula (nCr):
12C2 = (12!)/(2!(12-2)!) = (12!)/(2!10!) = (12 * 11)/(2 * 1) = 66.
The total number of ways to choose two students out of the total 22 is given by:
22C2 = (22!)/(2!(22-2)!) = (22!)/(2!20!) = (22 * 21)/(2 * 1) = 231.
Therefore, the probability of choosing two female students is: 66/231 ≈ 0.2857.
(b) Now, let's calculate the probability of choosing no more than 1 male student:
The number of ways to choose 2 students with no more than 1 male can be calculated by:
Number of ways to choose 0 male students: 12C2 = 66 (as calculated earlier).
Number of ways to choose 1 male student: 12C1 * 10C1 = 12 * 10 = 120.
Therefore, the total number of ways is: 66 + 120 = 186.
The probability of choosing no more than 1 male student is: 186/231 ≈ 0.8041.
(c) To calculate the probability of choosing same gender students, we need to calculate the probabilities of choosing both male and both female students, and then add them together.
Probability of choosing 2 males:
10C2 = (10!)/(2!(10-2)!) = (10!)/(2!8!) = (10 * 9)/(2 * 1) = 45.
Probability of choosing 2 females (calculated earlier): 66/231 ≈ 0.2857.
Therefore, the probability of choosing students with the same gender is: 45/231 + 66/231 ≈ 0.3450.
To compute the probabilities, we need to find the total number of possible outcomes and the number of favorable outcomes for each scenario.
(a) Probability of choosing two female students:
Total Possible Outcomes = Total number of students = 10 (males) + 12 (females) = 22
Favorable Outcomes = Number of ways to choose 2 female students from 12 = C(12, 2) = 66 (using combination formula)
Probability = Favorable Outcomes / Total Possible Outcomes = 66 / 22 = 3 / 11
(b) Probability of choosing no more than 1 male student:
Total Possible Outcomes = Total number of students = 10 (males) + 12 (females) = 22
Favorable Outcomes:
- Choosing 0 males and 2 females: C(12, 2) = 66
- Choosing 1 male and 1 female: Number of ways to choose 1 male from 10 and 1 female from 12 = 10 * 12 = 120
Total Favorable Outcomes = 66 (for 0 males and 2 females) + 120 (for 1 male and 1 female) = 186
Probability = Favorable Outcomes / Total Possible Outcomes = 186 / 22 = 93 / 11
(c) Probability of choosing same gender students:
Total Possible Outcomes = Total number of students = 10 (males) + 12 (females) = 22
Favorable Outcomes:
- Choosing 2 males: C(10, 2) = 45 (using combination formula)
- Choosing 2 females: C(12, 2) = 66 (using combination formula)
Total Favorable Outcomes = 45 (for 2 males) + 66 (for 2 females) = 111
Probability = Favorable Outcomes / Total Possible Outcomes = 111 / 22 = 5 / 2