independent events. events that do not have an affect on another event. examples: tossing a coin...

INDEPENDENT EVENTS

INDEPENDENT EVENTS

Events that do NOT have an affect on another event.

Examples:

Tossing a coin

Drawing a card from a deck

P(A, then B) = P(A) X P(B)

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

1. Drawing 2 sevens

2. Drawing an odd number, then an even.

3. Drawing a 3, then an even number.

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

1. Drawing 2 sevens

1 1

10 10

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

1. Drawing 2 sevens

1 1 1

10 10 100

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

2. Drawing an odd number, then an even.

5 5

10 10

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

2. Drawing an odd number, then an even.

5 5 25 1

10 10 100 4

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

3. Drawing a 3, then an even number.

1 5

10 10

Example

You draw from a hat slips of paper numbered 0 – 9. After drawing a slip of paper, you look at the number then replace it in the hat. Find the probability of:

3. Drawing a 3, then an even number.

1 5 5 1

10 10 100 20

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

1. P(Green, 6)2. P(Blue or yellow, 5)3. P(Red, odd)4. P(Not blue, 2)

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

1. P(Green, 6)1 1

4 6

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

1. P(Green, 6)1 1 1

4 6 24

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

2. P(Blue or yellow, 5)2 1

4 6

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

2. P(Blue or yellow, 5)2 1 2 1

4 6 24 12

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

3. P(Red, odd)1 3

4 6

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

3. P(Red, odd)1 3 3 1

4 6 24 8

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

4. P(Not blue, 2) 3 1

4 6

Example

You play a game in which you draw a card colored red, green, blue, or yellow. You then roll a number cube. Find the probability of:

4. P(Not blue, 2) 3 1 3 1

4 6 24 8

Example

A baseball player has a batting average of 0.300. The next batter has a batting average of 0.275. What is the probability both will get a hit the next time up to bat?

0.300 0.275 0.0825

This is just a little over 8% of the time.

ASSIGNMENT

12.5A: 1 – 7, 15 – 20, 32