1.5 Independent and Dependent Events

Flipping a Coin

Independent Event

Situations in which the occurrence or non-occurrence 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:

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)

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