Probability with combinations
Mr. Sauber needs to select five
students to compete in a scholars’
bowl. He decides to randomly select
students from a group of 4 seniors, 5
juniors, and 2 sophomores. What is
the probability that he will select two
seniors, two juniors, and one
sophomore?
Discrete Math Section 16.4
Use combinations to solve probability problems
A committee of three is to be
selected from 3 girls and 2 boys.
What is the probability of selecting
2 girls and one boy at random?
P(BGG) = (2/5)(3/4)(2/3) = 1/5
P(GGB) = (3/5)(2/4)(2/3) = 1/5
P(GBG) = (3/5)(2/4)(2/3) = 1/5
1/5 + 1/5 + 1/5 = 3/5
2nd method
Probability = 3C2 2C1
_________
5C3
= (3)(2) = 3/5
10
example
Five marbles are chosen at random from a bag
containing 4 white, 3 green and 5 black
marbles. What is the probability of choosing 2
white, 1 green, and 2 black marbles?
example
A carton contains 200 batteries, of which 3 are
defective. If a random sample of 5 batteries is
chosen, what is the probability that at least one of
them is defective?
(Calculate the probability that none are defective and use Complement Principle: 1 – P(not D) )
assignment
• Page 621
• Problems 3,6,8,10,16,19,20