Independent and Dependent Events

Slide 1

Independent Events

Whatever happens in one event has absolutely nothing to do with what will happen next because: 1. The two events are unrelated

OR

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

OR

3. 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.

Slide 2

Independent Events

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

P(even) = 1 2 P(vowel) = 1 5 (3 evens out of 6 outcomes) (1 vowel out of 5 outcomes) P(even, vowel) = 2 5 1 10 6 1 P S 5 2 O T 3 4 R

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.

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 first) = 6 14 or 3 7 P(black second) = 5 13 (There are 13 pens left and 5 are black)

THEREFORE………………………………………………

P(black, black) = 3  5 7 13 or 15 91

Slide 5

1.

TEST YOURSELF

Are these dependent or independent events?

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

Independent Events

Find the probability

• P(jack, factor of 12)

1 5

x

5 8

= 5 40 1 8

Slide 7

Independent Events

Find the probability

• P(6, not 5)

1 6

x

5 6

5 = 36

Slide 8

Dependent Events Find the probability

• P(Q, Q) • All the letters of the alphabet are in the bag 1 time • Do not replace the letter

1 26

x

0 25

= 0 650

0

Slide 9