Sunday
May 19, 2013

# Homework Help: Advanced Math

Posted by Patrick on Wednesday, June 10, 2009 at 10:07am.

Consider a class with 10 sophomores, 8 juniors, and 6 seniors. Two students are selected at random.
a) What is the probability of selecting 1 junior and 1 senior?
b) Find the odds of selecting two students who are not seniors.

A) 2/23
B) 51/92

Are these correct?

• Advanced Math - AUSTIN, Wednesday, June 10, 2009 at 10:25am

A=2/24

• Advanced Math - MathMate, Wednesday, June 10, 2009 at 10:58am

A) 4/23, B) correct

total number of possible permutations
= 24P2
= 24*23
= 552

a) What is the probability of selecting 1 junior and 1 senior?
There are two possibilities, a junior (J) followed by a senior (S),
JS=8*6/552=2/23
Similarly,
SJ=6*8/552=2/23
Thus total probability
= 2/23+2/23=4/23

b) Find the odds of selecting two students who are not seniors.
There are 10+8 = 18 students who are not seniors.
Probability for first draw
=18/24
probability for second draw
=17/23
Probability that both will occur
= 18/24*17/23
= 51/92

• Advanced Math - Reiny, Wednesday, June 10, 2009 at 11:09am

since the order does not matter it is best to do these with combinations.

you probably did (8/24)(6/23) = 2/23
that is the prob of picking a junior and then a senior, but the order could have been reversed
so the prob is 2(2/23) = 4/23

with combinations it would have been
C(8,1)*C(6,1)/C(24,2) = 48/273 = 4/23

for b)
odds in favour of some event
= Prob(event)/prob(not the event)

so prob(no seniors) = C(18,2)/C(24,2) = 153/276 = 51/92
then prob of "some" seniors = 1 - 51/92 = 41/92

the odds of selecting two students who are not seniors = 51:41

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