Probability – Single Events
Probability Rules for any Probabilistic Model:
1) Sum of the probability of all possible events is one; P(Events) = 1
2) All probabilities must be 0 ≤ P(Events) ≤ 1
3) P(Event) + P(Event’s Compliment) = 1
4) P(certainty – always happens) = 1 and P(impossibility – can’t happen) = 0
Basic Probability Concept: The probability of an event is the number of chances the
event has of occurring divided by the total number of all chances.
For example, on a 8-sided die we have a one in eight chance of getting an particular
outcome (roll a 2 for example). Once chance to get a 2 out of 8 total chances gives the
following: P(x=2) = 1/8 = 0.125
In the examples we will use is one six-sided die in the first few questions below.
1. What is the probability of rolling a “6”?
P(roll = “6”) = 1/6 = 0.17
2. What is the probability of rolling an even number?
P(roll = “2” or “4” or “6”) = 3/6 = 0.50
3. What is the probability of rolling less than a “3”?
P(roll = “1” or “2”) = 2/6 = 0.33
4. What is the probability of rolling something other than a “6”?
Use the complement rule: P(roll ≠ “6”) = 1 – P(roll = “6”) = 1 – 1/6 = 5/6 = 0.83
In the following examples, we are using a normal playing card deck of 52 cards; four suits
(two red – diamonds and heats and two black – clubs and spades) of 13 cards each; two
through ten, jack, queen and king (all known as face cards), and an ace.
5. What is the probability of drawing a black card?
P(draw = “club or spade”) = 26/52 = 0.5
6. What is the probability of drawing an ace?
P(draw = “ace”) = 4/52 = 1/13 = 0.08
7. What is the probability of drawing a heart?
P(draw = “heart”) = 13/52 = 1/4 = 0.25
Probability – Single Events Worksheet
1. Kyle rolls an eight sided dice; what is the probability that he rolls a “3”?
2. What is the probability that he rolls a nonprime number (4, 6, 8)?
3. What is the probability that he rolls an even number?
4. Harriet has a regular deck of cards and draws one card out. What is the probability that
it is a face-card?
5. What is the probability that she draws out a spade?
6. What is the probability that she draws out a non-face card?
7. Jon has a twenty-sided die from a D&D set. What is the probability that he rolls a “5”?
8. What is the probability that he rolls a “8” or less?
9. What is the probability that he rolls a “14” or more?