Math 1530 Walters State Comm College Review for Exam 2
1. In rolling a die, what is the probability of obtaining either a 5 or a 6?
1 1 1
(5 6) (5) (6)
6 6 3
P P P
∪ = + = + =
2. On four consecutive rolls of a die a 6 is obtained. What is the probability of obtaining a 6 on the 5
th
roll?
Events are independent …
1
(6)
6
P
=
3. Based on meteorological records, the probability that it will snow in a certain town on Jan 17 is 0.315. Find the probability
that it will not snow in that particular town on Jan 17.
The probability of the compliment of an event is: 1 – probability of the event = 1 – 0.315 = 0.685
4. In tossing a coin, what is the probability of obtaining HHHTH in that order in five tosses?
Events are independent …
5
1 1
( ) ( ) ( ) ( ) ( ) ( )
2 32
P H H H T H P H P H P H P T P H
∩ ∩ ∩ ∩ = ⋅ ⋅ ⋅ ⋅ = =
5. Consider a standard deck of 52 cards. Determine the following probabilities.
A. P(9 of clubs): 1/52
B. P(ace): 4/52 = 1/13
C. P(ace of spades and ace of hearts) in that order with and without replacement
1 1 1 1 1 1
: ; without:
52 52 2704 52 51 2652
with ⋅ = ⋅ =
D. P(3 aces) with and without replacement
1 1 1 1 1 1 1 1
: ; without:
13 13 13 2197 13 17 25 5525
with ⋅ ⋅ = ⋅ ⋅ =
E. P(ace, king, queen) in that order with and without replacement
3
1 1 1 4 2 8
: ; without: 0.000483
13 2197 13 51 25 16575
with = ⋅ ⋅ = ≈
6. An urn contains 20 red balls, 20 green balls, and 20 yellow balls. Suppose three balls are randomly selected. Find the
following probabilities.
A. P(3 red) with and without replacement
20 20 20 1 1 19 9 57
: ( ) ; without:
60 60 60 27 3 59 29 1711
with P red red red∩ ∩ = ⋅ ⋅ = ⋅ ⋅ =
