Posted by Patrick on Wednesday, June 10, 2009 at 10:07am.
A=2/24
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
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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