a class has 10 boys and 5 girls; three students are selected from the class at random one after other. the probability that the first two boys and the third is a girl??
Pr=(10/15)(9/14)(5/13)
10/15 * 9/14 * 5/13 = 15/91 = 0.165 (3sf)
To calculate the probability of selecting two boys followed by a girl from a class of 10 boys and 5 girls, we need to find the probability of each event occurring and then multiply those probabilities together.
Step 1: Find the probability of selecting a boy on the first pick.
There are 10 boys and 15 total students in the class (10 boys + 5 girls). So, the probability of selecting a boy on the first pick is:
P(boy on first pick) = 10/15
Step 2: Find the probability of selecting a boy on the second pick.
After selecting a boy on the first pick, there are now 9 boys left out of a total of 14 students remaining. So, the probability of selecting a boy on the second pick is:
P(boy on second pick) = 9/14
Step 3: Find the probability of selecting a girl on the third pick.
After selecting two boys on the first two picks, there are now 5 girls left out of a total of 13 students remaining. So, the probability of selecting a girl on the third pick is:
P(girl on third pick) = 5/13
Step 4: Multiply the probabilities together.
To find the probability of all three events happening (selecting two boys and then a girl), we multiply the individual probabilities together:
P(boy, boy, girl) = P(boy on first pick) * P(boy on second pick) * P(girl on third pick)
= (10/15) * (9/14) * (5/13)
Calculating the above expression gives us the probability of the first two picks being boys and the third pick being a girl.
To calculate the probability that the first two students selected are boys and the third student is a girl, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Since there are 10 boys and 5 girls in the class, there are a total of 15 students.
The first student can be any of the 15 students.
After the first student is selected, there are 14 students left.
The second student can be any of the remaining 14 students.
After the second student is selected, there are 13 students left.
The third student can be any of the remaining 13 students.
Therefore, the total number of possible outcomes is 15 * 14 * 13 = 2730.
Number of favorable outcomes:
Since we want the first two students to be boys and the third student to be a girl, we need to select 2 boys (out of the 10 available boys) and then select 1 girl (out of the 5 available girls).
The number of ways to select 2 boys from 10 is given by the combination formula:
C(10, 2) = 10! / (2! * (10 - 2)!) = 45.
The number of ways to select 1 girl from 5 is given by the combination formula:
C(5, 1) = 5! / (1! * (5 - 1)!) = 5.
Therefore, the number of favorable outcomes is 45 * 5 = 225.
Probability calculation:
The probability is calculated as the number of favorable outcomes divided by the number of possible outcomes:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 225 / 2730
Probability ≈ 0.08 or 8% (rounded to the nearest percentage).
So, the probability that the first two students selected are boys and the third student is a girl is approximately 8%.