Course :Title: Statistics 1 | Regular/ Fall Session 2025

Course Code: PSY-3111

Probability
Learning Objectives
● Defining Probability
● Rules of probability

Summary
Probability is the measure of the likelihood that an event will occur in a Random
Experiment.

Probability of two events occurring can be found by simply adding them (probability of either
event A or B occurring= probability of A + Probability of B). The formula of either A or B
occurring can also be written as: P(A or B) = P(A) + P(B), when the chance of A and B
occurring together is zero. When these two events are not mutually exclusive, we have to
minus the probability of both occurring so we don’t count them twice, and the formula
becomes: P(A or B) = P(A) + P(B) - P(A and B)

Definition of Probability
Probability is the measure of the likelihood that an event will occur in a Random
Experiment.

Rules of Probability
There are two rules of probability:

Addition Rule
So far we’ve been talking about the probability of just one event, but often there may be two or
more events that we want to consider, like what if you want to know the probability of picking a
purple OR a red skittle from a bag.The proportion of each color in a bag of Skittles is roughly
equal, 20% for each of the 5 colors.So let’s say you randomly select a Skittle without looking.For
this, we need the addition rule of probability. Since a Skittle can’t be two different colors at once,
the color possibilities are Mutually Exclusive.That means the probability of a Skittle being red
AND purple at the same time is 0. So, we can use the simplified addition rule which says that
the probability of getting a Red or Purple Skittle is the sum of the probability of getting a Red,
and the probability of getting a purple. I’m going to introduce a little notation. Instead of writing
out “the probability of Red” we can use the notation P(Red). The probability of getting a red OR
purple would then be written P(Red or Purple). So far we know what the probability of Red or
Purple is, P(Red) + P(Purple), or 0.2+0.2
That equals 0.40 or 40%. I like all skittles so the probability that I will get a skittle I
like is 0.2 + 0.2 +0.2 +0.2 +0.2. That’s 100%. Good odds! Red and Purple Skittles
are mutually exclusive, but not all the events we’re interested in are. For example,
if you roll a die and flip a coin, the probability of getting a tails is not mutually
exclusive of rolling a 6, since you can both roll a 6 and flip tails in the same
turn.Since P(tails or 6) ≠ 0, these two events are not mutually exclusive, and we’ll
need to adjust our addition rule accordingly.

The full version of the addition rule states that P(tails or 6) = P(tails) + P(6) - P(tails and 6).
When two things are mutually exclusive, the probability that they happen together is 0, so we
ignored it, but now the probability of both these things happening is not zero, so we’ll need to
calculate it. You can see here that there are 12 possible outcomes when flipping a coin and
rolling a die. There are 6 outcomes with a tails, and 2 outcomes with a 6. If we add all of those
together we get 8, but by looking through the chart, we can tell that there are only 7 possible
outcomes that have either a tails or a 6.When we count T’s and 6’s independently, we double
count the outcomes that have bothIf we didn’t subtract off the probability of (tails and 6), we
would double count it.

Multiplication Rule We can simply multiply the probabilities of two events to get the
probability of both events happening. For example, th

PRACTICE QUESTIONS
1. In a bag, there are 5 red balls and 7 black balls. What is the probability of getting a black
ball?
2. If two coins are tossed simultaneously, what is the probability of getting exactly two
heads?
3. What is the probability of getting an even number on rolling a six-sided dice numbered
from 1 to 6?
4. What is the probability of getting 2 sixes while rolling a six sided dice?
5. In a bag there are 8 red candies and 6 yellow candies, you have to pick one candy.
What is the probability of getting a red candy?
6. A card is drawn at random from a well-shuffled pack of cards numbered 1 to 20. Find the
probability of getting a number divisible by 3
7. Find the probability of scoring a total of more than 7, when two dice are thrown.
8. An event has a 25% chance of occurring. What is the chance of it not occurring?
9. Event A has a 50% chance of occurring, and Event B has a 50% chance of
occurring. What is the probability that Event A and Event B occur, assuming that the
events are independent?
 10. Event A has a 50% chance of occurring, and Event B has a 50% chance of
occurring. What is the probability that Event A or Event B occurs, assuming that they
are mutually exclusive?
11. Event A has a 50% chance of occurring, and Event B has a 50% chance of
occurring. What is the probability that Event A or Event B occurs, assuming that they
are not mutually exclusive?
12. Event A has a 20% chance of occurring, and Event B has a 20% chance of
occurring. What is the probability that Event A or Event B occurs, assuming that they
are mutually exclusive?

Reference
Probability Part 1: Rules and Patterns: Crash Course Statistics #13