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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