The document contains 5 questions about probability. Question 1 asks for the probability of getting exactly 2 green dresses if 6 dresses are sold from a rack containing 15 dresses with different colors. Question 2 asks for the probability of a couple having at least 2 girls if they intend to have 4 children. Question 3 asks for the probability that a randomly chosen vehicle from a car lot is an SUV given that the vehicle has air conditioning. Question 4 asks for the probability that exactly one of two randomly drawn razor blades from a box is defective. Question 5 asks for the probability of getting exactly 2 heads if a biased coin is tossed 6 times with the probability of heads being 2/5.

1. Probability Workshop
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2. Question 1
A rack contains 15 dresses. Five of the dresses are blue, six are green, and four
are yellow. If selling each of the dresses is equally likely, what is the probability
that if six dresses are sold, exactly two will be green?
2

3. A rack contains 15 dresses. Five of the dresses are blue, six are green, and four are
yellow. If selling each of the dresses is equally likely, what is the probability that if six
dresses are sold, exactly two will be green?
choose 4 from the
choose 2 green
dresses that are not
green
P(2G) = 6C2 9C4
choosing 6 dresses
15C6 from the rack
= 15 126
5 005
= 1 890
5 005
= 0.377 or 37.8 %
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4. Question 2
A couple intends to have 4 children. Assume that having a boy or a girl
are equally likely events. Find the probability that the couple has atleast
2 girls.
4

5. A couple intends to have 4 children. Assume that having a boy or a girl are equally
likely events. Find the probability that the couple has atleast 2 girls.
Choose atleast 2 girls, it could be 2 girls and 2 boys
or 3 girls and 1 boy, or 4 girls then add them.
P (2G) = 4C2 + 4C3 + 4C4
4
(2C1) Choose the gender then multiply it 4
times because there are four children.
= 11
16
5

6. Question 3
In a car lot, 25% of the inventory are SUV's, and 75% are passenger cars. 80%
of SUV's, and 65% of the passenger cars, have air conditioning. What is the
probability that a chosen vehicle will be an SUV given the vehicle has air
conditioning?
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7. In a car lot, 25% of the inventory are SUV's, and 75% are passenger cars.
80% of SUV's, and 65% of the passenger cars, have air conditioning. What
is the probability that a chosen vehicle will be an SUV given the vehicle has
air conditioning?
P(SA) = (.25) (.80) = .2
S ­ SUV
P(PA) = (.75) (.35) = .4875
P ­ Passenger Car
P (SA)
A ­ with AC
P(S|A) =
N ­ no AC A .80 P(SA) + P(PA)
.2
S =
N .20
.25 (.2) + (.4875)
A .65 = .281
P
.75
N .35
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8. Afternoon Class
continuation of the Probability Workshop
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9. Question 4
A box of eight razor blades contains two defective blades. If two blades
are drawn at random, with the first not replaced, what is the probability
that exactly one of the two blades will be defective?
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10. Solution:
A box of eight razor blades contains two defective blades. If two blades are drawn at
random, with the first not replaced, what is the probability that exactly one of the two
blades will be defective?
2
6
= 12
N = Not Defective ND = 7 56
8
D = Defective
2 6
5 12
N DN = 7 = 56
7
8
N 12 12
= 56 + 56
2
6
D 7
8
24
N6 = 56
7
D
2
3
=
1
D
8
7
7
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11. Question 5
If a biased coin is tossed 6 times, what is the probability of obtaining
exactly 2 heads if the probability of getting heads on any one is 2/5?
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12. Solution:
If a biased coin is tossed 6 times, what is the probability of obtaining
exactly 2 heads if the probability of getting heads on any one is 2/5?
( )( ) ( )( )( )( )
H = Heads 3
3
3 3
2 2
HHTTTT
T = Tails 5
5
5 5
5 5
6! 2 4
( )( ) 3
2
5
5
2!4!
4 tails
number of different
2 heads
ways that you can get 2
heads and 4 tails
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