A class roster includes 24 males students and 15 female students who are IT majors. If 4 students from the group are selected to represent IT majors at a University meeting, what is the probability 2 will be male and 2 will be female?
2male=2/24=1/12 2female=2/15
This is actually the correct answer:
(24C2)*(15C2) 276*105 28980
_____________= ________ =________ =0.35
(39C4) 82251 82251
Sorry the spacing for the above answer shifted when I posted but the answer is 0.352
To find the probability of selecting 2 male students and 2 female students, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Calculate the total number of IT majors in the class roster.
Total IT majors = Number of male IT majors + Number of female IT majors
Total IT majors = 24 + 15
Total IT majors = 39
Step 2: Calculate the number of possible outcomes for selecting 4 students from the group of IT majors.
Number of possible outcomes = Combination of total IT majors taken 4 at a time
Number of possible outcomes = C(39, 4) = 39! / (4! * (39-4)!)
Number of possible outcomes = 822,155
Step 3: Calculate the number of favorable outcomes for selecting 2 male students and 2 female students.
Number of favorable outcomes = Combination of male IT majors taken 2 at a time * Combination of female IT majors taken 2 at a time
Number of favorable outcomes = C(24, 2) * C(15, 2) = (24! / (2! * (24-2)!) * (15! / (2! * (15-2)!)
Number of favorable outcomes = 276 * 105
Number of favorable outcomes = 28,980
Step 4: Calculate the probability.
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 28,980 / 822,155
Probability ≈ 0.0353 or 3.53%
Therefore, the probability of selecting 2 male students and 2 female students from the group of IT majors is approximately 0.0353 or 3.53%.