Independent Events

Probability of Dependent and Independent Events

By Marilou Fajardo

​Mutually Exclusive Events

or

Not Mutually Exclusive Events

​Review

Multiple Choice

Rolling a prime number or rolling an even number in a six-sided die.

• Mutually Exclusive

• Non Mutually Exclusive

Multiple Choice

Getting an odd number or a perfect square from a box with chips numbered 1-20.

• Mutually Exclusive

• Non Mutually Exclusive

Multiple Choice

Turning left or right when crossing on the street.

• Mutually Exclusive

• Non Mutually Exclusive

Multiple Choice

Playing an online game or answering a quiz.

• Mutually Exclusive

• Non Mutually Exclusive

Multiple Choice

Picking a face card or picking a heart in a standard deck of cards.

• Mutually Exclusive

• Non Mutually Exclusive

​ACTIVITY - POLL TIME!

Poll

Studying hard, getting a high grade.

• 1st event affects the 2nd event

• 1st event does NOT affect the 2nd event

Poll

Eating a lot, gaining weight.

• 1st event affects the 2nd event

• 1st

Poll

Buying a lottery ticket, finding a coin on the floor.

• 1st event affects the 2nd event

• 1st event does NOT affect the 2nd event

Poll

Playing computer games, submitting all assignments on time.

• 1st event affects the 2nd event

• 1st event does NOT affect the 2nd event

Poll

Tossing a coin, rolling a die.

• 1st event affects the 2nd event

• 1st event does NOT affect the 2nd event

Poll

Attending a singing lesson, raining today.

• 1st event affects the 2nd event

• 1st event does NOT affect the 2nd event

​Dependent Events – two or more events in

which the outcome of one event does affect

the outcome of the other event.

​Independent Events – two or more events in

which the outcome of 1 event does not affect

the outcome of the other event.

​Examples

​1. There are two red balls, 4 yellow balls, and 1 blue ball in a box.

Two balls are drawn randomly  one by one with replacement.

Find the probability that two yellow balls are drawn.

​2.  Three cards are chosen at random from a deck of 52 cards

without replacement. What is the probability of choosing a

king, a queen, and an ace in order?

​Examples

​Solution:

​P(king,queen,ace) = P(king) x P(queen after king) x P(ace after queen)​

​3.  George met Susie in a dating app and they got married.  George is heterozygous for his brwon eyes , but Susie has blue eyes.  If they will have 2 children, what is the probability that the first has blue eyes and the second has brown eyes?

​Examples

​Solution:

P(blue eyes, brown eyes) = P(blue) x P(brown)​

​4.  There are 10 candidates that are divided into two slates of senators. 

The first slate consists of 6 members and the second slate consist of 4 ​ members.  June will randomly choose 2 and vote. What is the probability that June will vote one from the first slate and another from the second slate?

Solution:

P(1st slate, 2nd slate) = P(1st slate) x P(2nd slate)​

​Examples

​PRACTICE EXERCISES

-PADLET-​

​Two events are independent if the occurrence of one event gives no information if the other event will occur; that is the events have no influence on each other.  If two events A and B, then the probability of both events occurring is the product of the probability of A and the probability of B.  In symbol,

P(A and B) = P(A) x P(B).

​When the outcome of one event affects the outcome of another event, they are dependent events.  If two events, A and B, are dependent, then the probability of both events occurring is the product of the probability of A and the probability of B after A occurs.  In symbols, P(A and B) = P(A) x P(B after A).

​ASSESSMENT #8

-Google Form-​

How do you feel about the lesson on Probability of Dependent and Independent Events?