Probability Of Independent And Dependent Events Worksheet Page 2
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Using a Complement to Find a Probability
E X A M P L E 3
Trading Cards
You collect hockey trading cards. For one team there are
25 different cards in the set, and you have all of them
except for the starting goalie card. To try and get this card,
you buy 8 packs of 5 cards each. All cards in a pack are
different and each of the cards is equally likely to be in a
given pack. Find the probability that you will get at least
one starting goalie card.
S
OLUTION
In one pack the probability of not getting the starting goalie card is:
C
24
5
P(no starting goalie) =
C
25
5
Buying packs of cards are independent events, so the probability of getting at least
one starting goalie card in the 8 packs is:
P(at least one starting goalie) = 1 º P(no starting goalie in any pack)
8
C
2
4
5
= 1 º
C
2
5
5
≈ 0.832
Solving a Probability Equation
E X A M P L E 4
Manufacturing
A computer chip manufacturer has found that only 1 out of 1000 of its chips is
defective. You are ordering a shipment of chips for the computer store where you
work. How many chips can you order before the probability that at least one chip is
defective reaches 50%?
S
OLUTION
Let n be the number of chips you order. From the given information you know that
S
H
TUDENT
ELP
9
9
9
P(chip is not defective) =
= 0.999. Use this probability and the fact that each
Look Back
1
0
0
0
For help with solving
chip ordered represents an independent event to find the value of n.
exponential equations,
P(at least one chip is defective) = 0.5
Write given assumption.
see p. 501.
1 º P(no chips are defective) = 0.5
Use complement.
n
1 º (0.999)
= 0.5
Substitute known probability.
n
º(0.999)
= º0.5
Subtract 1 from each side.
n
(0.999)
= 0.5
Divide each side by –1.
l
og
0
.
5
n =
Solve for n.
lo
g
0.
9
9
9
n ≈ 693
Use a calculator.
If you order 693 chips, you have a 50% chance of getting a defective chip.
Therefore, you can order 692 chips before the probability that at least one chip
is defective reaches 50%.
12.5 Probability of Independent and Dependent Events
731
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