Lesson 11.9 Independent and Dependent Events. Goal Statement will find the probability that event A...

Lesson 11.9

Independent and Dependent Events

Goal Statement

will find the probability that event A and event B occur

Motivating the Lesson

Place 5 prizes in a bag (with 2 highly desired prizes). Ask what the probability of selecting the favored prizes is. (2/5)

Select one of the favored prizes and remove from the bag. Ask students for the prob that the next prize selected will be the favored one. (1/4)

Discuss why this prob depends on the result of the first selection.

Dictionary dependent events:

-when getting one event affects the probability of getting the other event

independent events:

-when getting one event does not affect the probability of getting the other event

LET’S TRY

Try

3. You randomly draw a marble from a bag. Then you draw a second marble without returning the first one.

4. You roll a 3 on a number cube, then you roll a 3 again.

Independent EventsYou roll a number cube and toss a coin.

a) Why is this an independent event experiment?

b) What is the probability of rolling an odd number and getting heads?

Independent EventsYou roll a number cube and toss a coin.

a) Why is this an independent event experiment?

b) What is the probability of rolling an odd number and getting heads?

P(odds, heads) = 3/6 x ½

= 3/12 or ¼

Finding the Probability of Independent Events

A computer randomly generates 4-digit passwords. Each digit can be used more than once.

a) Why is this an independent event experiment?

b) What is the probability that the first two digits in your password are both 1?

Finding the Probability of Independent Events

A computer randomly generates 4-digit passwords. Each digit can be used more than once.

a) Why is this an independent event experiment?

b) What is the probability that the first two digits in your password are both 1?

c) What is the probability that all four digits are 1?

If each digit can be used only once, are the events still independent? Explain.

A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble.

Are these dependent or independent events? Explain to a partner.

A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. What makes this more complicated to calculate?

A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. What makes this more complicated to calculate?

Because the events are dependent, the probability that you draw a blue marble after drawing a red marble is written as: P(blue given red)

A bag contains 5 red marbles and 5 blue marbles. You randomly draw a marble, then you randomly draw a second marble without replacing the first marble. What makes this more complicated to calculate?

Because the events are dependent, the probability that you draw a blue marble after drawing a red marble is written as: P(blue given red)

Dictionary

Probability of Dependent Events

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

LET’S TRY

A jar of jelly beans contains 50 red jelly beans, 45 yellow jelly beans, and 30 green jelly beans. Eric reaches into the jar and randomly select a jelly bean, then select another without putting the first jelly bean back.

a) Are these dependent or independent events?

b) What is the probability that Eric draws two red jelly beans?

LET’S TRY

A jar of jelly beans contains 50 red jelly beans, 45 yellow jelly beans, and 30 green jelly beans. Eric reaches into the jar and randomly select a jelly bean, then select another without putting the first jelly bean back.

a) Are these dependent or independent events?

b) What is the probability that Eric draws two red jelly beans?

P(red and then red) = P(red) p P(red given red)

Show Ms Schones

An Advisory class consists of 6 girls and 7 boys. To select MSSC reps, two students are chosen at random one at a time. The first student chosen is a girl. What is the probability that both students who are selected are girls?

Homework

Green:

pgs.637 – 638:

#1 – 8 (all except 5), 9 – 15 (all), 17

Blue:

11.9 Blue WS