Please try to Work out these Extra Problems for Practice.
If you do not understand how to solve these problems, please refer to the learning packet (above),
--or the websites that I have cited (summary box).
Answers are given in the text box below!
Example 1: With Replacement
What is the probability of tossing a fair coin twice in a row and getting heads both times?
Example 2: Without Replacement
If you draw two cards from the deck without replacement, what is the probability that they will both be aces?
Example 3: List out the outcomes, probability of events, whether its mutually exclusive or all inclusive, sample space, and sample points
A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? of rolling an odd number?
Outcome:
Probabilities of Events:
Mutually Exclusive/All Inclusive:
Sample Space:
Sample Points:
Example 4: Events
Suppose we draw a card from a deck of playing cards. What is the probability that we draw a spade?
P(?)=?
Example 1: With Replacement
Answer: Since the probability of tossing a head (independent events) is 1/2 each time P(HH) = (1/2)(1/2) = 1/4.
Example 2: Without Replacement
Answer: P(AA) = (4/52)(3/51) = 1/221.
Example 3:
Answer:
Outcome: The possible outcomes of this experiment are 1, 2, 3, 4, 5 and 6.
Probabilities of Events:
P(1) = # of ways to roll a 1 = 1
total # of sides 6
P(2) = # of ways to roll a 2 = 1
total # of sides 6
P(3) = # of ways to roll a 3 = 1
total # of sides 6
P(4) = # of ways to roll a 4 = 1
total # of sides 6
P(5) = # of ways to roll a 5 = 1
total # of sides 6
P(6) = # of ways to roll a 6 = 1
total # of sides 6
Mutually Exclusive or All Inclusive: Mutally Exclusive
(since only one number can appear on the top of the dice)
Sample Space: S= {1,2,3,4,5,6}
Sample Points: The sample points are 1,2,3,4,5,6
or this experiement has 6 sample points
Example 4: Events
Answer: The sample space of this experiment consists of 52 cards, and the probability of each sample point is 1/52. Since there are 13 spades in the deck, the probability of drawing a spade is
P(Spade) = (13)(1/52) = 1/4
