INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin...
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Transcript of INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin...
![Page 1: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/1.jpg)
INDEPENDENT EVENTS
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INDEPENDENT EVENTS
Events that do NOT have an affect on another event.
Examples:
Tossing a coin
Drawing a card from a deck
![Page 3: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/3.jpg)
P(A, then B) = P(A) X P(B)
![Page 4: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/4.jpg)
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.
![Page 5: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/5.jpg)
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
![Page 6: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/6.jpg)
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
![Page 7: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/7.jpg)
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
![Page 8: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/8.jpg)
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
![Page 9: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/9.jpg)
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
![Page 10: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/10.jpg)
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
![Page 11: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/11.jpg)
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)
![Page 12: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/12.jpg)
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
![Page 13: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/13.jpg)
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
![Page 14: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/14.jpg)
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
![Page 15: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/15.jpg)
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
![Page 16: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/16.jpg)
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
![Page 17: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/17.jpg)
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
![Page 18: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/18.jpg)
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
![Page 19: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/19.jpg)
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
![Page 20: INDEPENDENT EVENTS. Events that do NOT have an affect on another event. Examples: Tossing a coin Drawing a card from a deck.](https://reader036.fdocuments.in/reader036/viewer/2022062409/5697bfc91a28abf838ca9057/html5/thumbnails/20.jpg)
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.
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ASSIGNMENT
12.5A: 1 – 7, 15 – 20, 32