3 people are selected at random without replacement out of 12 girls and 3 boys. What is the probability of selecting all girls?
Probability that all events would occur is found by multiplying the probabilities of the individual events.
12/15 * 11/14 * 10/13 = ?
12/15
To find the probability of selecting all girls, we need to determine the number of ways this can happen and divide it by the total number of possible outcomes.
First, let's calculate the total number of ways to select 3 people out of 15 (12 girls + 3 boys) without replacement. This can be done using the combination formula:
C(n, r) = n! / (r!(n - r)!)
where:
n is the total number of objects (15)
r is the number of objects being chosen (3)
Using this formula:
C(15, 3) = 15! / (3!(15 - 3)!) = 15! / (3!12!) = (15*14*13) / (3*2*1) = 455
Now, let's determine the number of ways to select all girls. Since we want to select 3 girls out of the 12 available, we can use the combination formula again:
C(12, 3) = 12! / (3!(12 - 3)!) = 12! / (3!9!) = (12*11*10) / (3*2*1) = 220
Finally, we can calculate the probability of selecting all girls by dividing the number of ways to select all girls by the total number of possible outcomes:
P(all girls) = C(12, 3) / C(15, 3) = 220 / 455 = 44 / 91 ≈ 0.4835
Therefore, the probability of selecting all girls is approximately 0.4835 or 48.35%.