1.5 Independent and
Dependent Events
Flipping a Coin
Independent Event

Situations in which the occurrence or nonoccurrence of one event has no influence on the
probability of the other event occurring.
2 Aces in here
Dependent Events
 The
occurrence or non-occurrence of one
event influences the probability of the
other event occurring.
Independent or Dependent

Richards has a container with 5 people names in
it. The first name he draws out gets first prize.
The second name he draws out get second price.

Are these dependent or independent events?
Pencils

Olivia has four highlighting pens in her pencil case: two
yellow, one orange, and one blue. She reaches into her
pencil case and randomly chooses a highlighter. After she
uses it, she immediately replaces it in the case so it can
be used again. What is the probability that she will
choose:

Two yellow highlighters?

A yellow highlighter followed by a blue highlighter?
Finding Probabilities of Compound
Events

Answer the same questions from last slide using another
method.
Multiplicative Principle for Independent
Events

AKA Fundamental Counting Principle

The probability of two independent events, A and B, occurring is:
𝑃 𝐴 𝑎𝑛𝑑 𝐵 = 𝑃 𝐴 ∗ 𝑃(𝐵)
Key word here is “AND”……. Prob of A AND B
My New Game

Is my Game Fair?

Player A wins a point if a spinner lands on red AND an even number is rolled

Player B wins a point if the spinner lands on yellow or green and a composite
number is rolled.
Drawing Cards

What is the probability of a King?

Two Aces and Two Kings are in my hand.
Conditional Probability

Probability of a second event occurring given that the first event occurred.
Multiplicative Principle for Dependent
Events

For Dependent Events, The probability of each outcome can change
“depending” and previous outcome.

Probability of (A and B) = P(A) x Prob(B Given A)
𝑃 𝐴 𝑎𝑛𝑑 𝐵 = 𝑃 𝐴 ∗ 𝑃(𝐵|𝐴)
Those Dang Telemarketers

How Much did the Telemarketer sell in 1000 calls?

The experiment probability of a call receiver staying on the line for at least a
minute was 16%

The conditional probability of a call resulting in a sale, given that they
receiver stayed on the line for more than a minute was 10%

No sales were made if the call hung up right away.
Assignment

Page 53 #’s 1-5, 7,11