Independent and Dependent Events

Slide 1

Independent EventsWhatever happens in one event has absolutely nothing

to do with what will happen next because:

1. The two events are unrelatedOR

2. You repeat an event with an item whose numbers will not change (eg.: spinners or dice)

OR3. You repeat the same activity, but you

REPLACE the item that was removed.

The probability of two independent events, A and B, is equal to the probability of event A times the probability of event B.

P(A, B) = P(A) P(B)Slide 2

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Example: Suppose you spin each of these two spinners. What is the probability of spinning an even number and a vowel?

P(even) =

P(vowel) =

P(even, vowel) =

Independent Events

Slide 3

Dependent Event

• What happens the during the second event depends upon what happened before.

• In other words, the result of the second event will change because of what happened first.

The probability of two dependent events, A and B, is equal to the probability of event A times the probability of event B. However, the probability of event B now depends on event A.

P(A, B) = P(A) P(B)Slide 4

Dependent Event

Example: There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take another pen without replacing the first, what is the probability that you will get 2 black pens?

P(black second) =

P(black first) =

P(black, black) =

THEREFORE………………………………………………

Slide 5

TEST YOURSELFAre these dependent or independent events?

1. Tossing two dice and getting a 6 on both of them.

2. You have a bag of marbles: 3 blue, 5 white, and 12 red. You choose one marble out of the bag, look at it then put it back. Then you choose another marble.

3. You have a basket of socks. You need to find the probability of pulling out a black sock and its matching black sock without putting the first sock back.

4. You pick the letter Q from a bag containing all the letters of the alphabet. You do not put the Q back in the bag before you pick another tile.

Slide 6

Find the probability

• P(jack, factor of 12)x =

Independent Events

Slide 7

Find the probability

• P(6, not 5)

x =

Independent Events

Slide 8

Find the probability• P(Q, Q)• All the letters of the

alphabet are in the bag 1 time

• Do not replace the letter

x =

Dependent Events

Slide 9