1. (1) Twelve people, including you, are member of a choir. The
choir director is going to choose three members to attend a
workshop. The probability you and two other members will be
chosen is:
d.) 1
c.) 1
a.) 1 b.) 3
10
12
4 10
1
How we get ?
4
probability that two other
probability that you are
member will be chosen
included in the workshop
1 C 1 11 C 2 55 1
= =
C 3 220 4
12
probability that 3 members
will be choose from 12 members

2. (2) Rex is playing a guessing game. The probability he will guess
each question correct is 0.3.What is the probability he will guess
exactly 5 out 10 questions correctly?
a.) 0.15 b.) 0.10 c.) 0.29 d.) 0.80
How we get 0.10?
R R R R R W W W W W
(0.3)(0.3)(0.3)(0.3)(0.3) (0.7)5
probability of getting
probability of
probability of
5 correct out
wrong answers
right answers
of 10 questions
(0.7)5
(0.3)5
C 5
10
0.00243 0.16807
252
0.1029 or 0.10

3. (3) You choose four digits from the numbers 0­9 ( ten digits in
total ), with no repeated digits. To win a prize, only two of your
numbers need to match the four selected by a computer. The
probability, correct to the nearest hundredth, that you will win a
prize is:
choosing 2 numbers from 4
choosing 3 numbers from
numbers multiply by
4 numbers multiply by
choosing 4
chooosing 2 numbers
choosing 1 number from
digit number
from 6 remaining numbers
6 remaining numbers
4 C 3 6 C 1 4 C 2 6 C 2
4 C 4
+
+
10 C 4
10 C 4 10 C 4
probability of choosing 4 digit number from 10 digit number
+
0.0048 +
0.1143 0.4286
0.5476
54.76%

4. (4) The serial number of a $10 bill contains 8 digits. If your
$10bill contains the digit 7 at least once, you win a prize. What
is the probability that your $10 bill will win?
P ( no. 7's) = (0.9)8
P (at least one 7) = 1 ­ (0.9)8
= 0.5695
= 56.95%

5. (5) John takes a lunch to school on two days, and on the other
three days he buys it. If he takes lunch he is late for his period 4
class 15% of the time, but if he buys it he is late 35% of the time.
first we can make a tree diagram and then make a sample space:
legend:
TL ­ Take Lunch
L 0.15 P (TL L) = 0.21
B ­ Buy lunch
L ­ Late
TL
N ­ Not late N0.85
2 P ( TL N) = 0.39
5
L 0.35
P ( B L ) = 0.06
B
N0.65
3
P ( B N ) = 0.34
5

6. a.) What is the probability that John arrives on time?
we have to add the probability that John take a lunch and
not late and the probability that John buy his lunch and not
late
P ( TL N) + P ( B N)
+ 0.34
0.39
P ( arrive on time ) = 0.73
= 73%

7. (b) If John was late, what is the probability that he took his
lunch to school?
P ( TL L)
=
P ( TL L)
P ( TL L) + P (B L)
0.06
= 0.06 + 0.21
0.06
= 0.27
= 0.2222
= 22.2%