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# Probability - Independent & Dependent Events

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### Probability - Independent & Dependent Events

1. 1. Using Probability
2. 2. Independent Events <ul><li>Result of the first draw does not effect the outcome of the second draw. </li></ul><ul><li>Ex: </li></ul><ul><ul><li>Event A - I draw a card from the bag. Then I put the card back in the bag. </li></ul></ul><ul><ul><li>Event B – I draw from the very same cards. </li></ul></ul>
3. 3. Independent Events <ul><li>If A & B are independent events, then I can find the probability of A and then B happening. </li></ul><ul><li>Multiply the events to find the probability of both events. </li></ul><ul><li>Formula </li></ul><ul><ul><li>P(A & B) = P(A) x P(B) </li></ul></ul>
4. 4. Independent Events <ul><li>Example: </li></ul><ul><li>You have a bag of 15 scrabble tiles. </li></ul><ul><li>3 of the tiles are the letter O. </li></ul><ul><li>What is the probability of getting an O ? </li></ul><ul><li>3/15 </li></ul><ul><li>2 of the tiles are the letter U . </li></ul><ul><li>What is the probability of getting an U ? </li></ul><ul><li>2/15 </li></ul>
5. 5. Independent Events <ul><li>What is the probability of getting O and then U ? </li></ul><ul><li>P(O) x P(U) </li></ul><ul><li>3/15 x 2/15 </li></ul><ul><li>2/75 </li></ul>
6. 6. Independent Events <ul><li>Example: </li></ul><ul><li>You have a 52 cards. </li></ul><ul><li>12 of the cards are the face cards . </li></ul><ul><li>What is the probability of getting a face card? </li></ul><ul><li>12/52 </li></ul><ul><li>4 of the cards are the Aces. </li></ul><ul><li>What is the probability of getting an Ace? </li></ul><ul><li>4/52 </li></ul>
7. 7. Independent Events <ul><li>What is the probability of getting a face card and then an Ace? </li></ul><ul><li>P(face card) x P(Ace) </li></ul><ul><li>12/52 x 4/52 </li></ul><ul><li>3/169 </li></ul>
8. 8. Dependent Events <ul><li>When you don’t replace the first item before drawing the second item, the events are dependent. </li></ul><ul><li>Formula: </li></ul><ul><ul><li>P(A&B) = P(A) x P(B after A) </li></ul></ul>
9. 9. Dependent Events <ul><li>Example: </li></ul><ul><li>You have a bag of 15 scrabble tiles. </li></ul><ul><li>3 of the tiles are the letter O. What is the probability of getting an O on the first draw? </li></ul><ul><li>3/15 </li></ul><ul><li>2 of the tiles are the letter U . What is the probability of getting an U if you didn’t replace the O ? </li></ul><ul><li>2/14 </li></ul>
10. 10. Dependent Events <ul><li>What is the probability of getting O and then U if you don’t replace the O ? </li></ul><ul><li>P(O) x P(U after O) </li></ul><ul><li>3/15 x 2/14 </li></ul><ul><li>1/35 </li></ul>
11. 11. Dependent Events <ul><li>Example: </li></ul><ul><li>You have a 52 cards. </li></ul><ul><li>12 of the cards are the face cards . What is the probability of getting a face card? </li></ul><ul><li>12/52 </li></ul><ul><li>4 of the cards are the Aces. What is the probability of getting an Ace if you don’t replace the face card? </li></ul><ul><li>4/51 </li></ul>
12. 12. Dependent Events <ul><li>What is the probability of getting a face card and then an Ace without replacing the face card? </li></ul><ul><li>P(face card) x P(Ace after face) </li></ul><ul><li>12/52 x 4/51 </li></ul><ul><li>4/221 </li></ul>
13. 13. Review <ul><li>Describe how to find the probability of two independent events. </li></ul><ul><li>Describe how to find the probability of two dependent events. </li></ul>