SOLUTION: A committee of 3 persons is selected at random from a group of 5 mathematicians and 8 physicists. What is the probability that all 3 are mathematicians?
A.
0.0350
B.
1/3
Algebra ->
Probability-and-statistics
-> SOLUTION: A committee of 3 persons is selected at random from a group of 5 mathematicians and 8 physicists. What is the probability that all 3 are mathematicians?
A.
0.0350
B.
1/3
Log On
Question 1098788: A committee of 3 persons is selected at random from a group of 5 mathematicians and 8 physicists. What is the probability that all 3 are mathematicians?
A.
0.0350
B.
1/3
C.
3/13
D.
15
You can put this solution on YOUR website! Since we want the probability that all three are mathematicians, we don't need to worry about the order in which they are chosen.
The probability that the first one selected is a mathematician is 5/13.
The probability that the second one selected is a mathematician is 4/12.
The probability that the third one selected is a mathematician is 3/11.
The probability that all three are mathematicians is (approximately).
...or you can use the nCr ("n choose r") concept to find the answer.
The total number of ways of choosing 3 of the 13 people is 13C3 = 286; the number of ways of choosing 3 of the 5 mathematicians is 5C3 = 10; so the probability that the 3 people chosen are all mathematicians is .
