405331168-PPT-Independent-and-Dependent.pptx

probability

1. Probability Independent and Dependent Events

2. Activity Reviewing the lessons, getting a perfect score on the exam. Throwing a die, drawing a card from a standard deck. Playing mobile games, studying and answering the learning module. Eating too much sugary foods, getting enough sleep. Getting a tail on the first coin, head on the second coin. YES YES YES NO NO

3. Independent Events Two events are said to be independent if the first event does not affect the probability of the second. If two events , A and B, are independent, then probability of both events occurring is the product of the probability of A and probability of B.

4. Independent Events Note: “ AND ” means to MULTIPLY ! There’s a replacement

5. INDEPENDENT EVENT FORMULA P(A and B) = P(A)  P(B)

6. Example 1 A coin is tossed and a 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die. P(Head and 3) P(A and B) = P(A)  P(B)

7. Example 2 A card is chosen at random from a deck of 52 cards. It is then replaced and a second card is chosen. What is the probability of choosing a jack and an eight? P(Jack and 8) P(A and B) = P(A)  P(B)

8. Example 3 A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and a yellow marble? P(Green and Yellow) P(A and B) = P(A)  P(B)

9. Example 4 A school survey found that 9 out of 10 students like pizza. If three students are chosen at random with replacement , what is the probability that all three students like pizza? P(Like and Like and Like)

10. Dependent Events Two events are said to be dependent if the first event AFFECTS the probability of the second event. If two events, A and B, are dependent, then probability of both events occurring is the product of the probability of A and probability of B after A occurs.

11. Dependent Events Note: Usually you will see the words “ without replacing ” “ AND ” still means to MULTIPLY ! (B following A) means that the event B occurs after event A has already happened/occurred

12. DEPENDENT EVENT FORMULA P(A and B) = P(A)  P(B following A)

13. Example 5 A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. A second marble is chosen without replacing the first one. What is the probability of choosing a green and a yellow marble? P(Green and Yellow) P(A and B) = P(A)  P(B following A)

14. Example 6 An aquarium contains 6 male goldfish and 4 female goldfish. You randomly select a fish from the tank, do not replace it , and then randomly select a second fish. What is the probability that both fish are male? P(Male and Male) P(A and B) = P(A)  P(B following A)

15. Example 7 A random sample of parts coming off a machine is done by an inspector. He found that 5 out of 100 parts are bad on average. If he were to do a new sample, what is the probability that he picks a bad part and then, picks another bad part if he doesn’t replace the first? P(Bad and Bad) P(A and B) = P(A)  P(B following A)

16. Assess Your Knowledge!

17. A coin is flipped, and a die is rolled. What is the probability of getting heads on the coin and a 4 on the die ? A bag contains 3 red balls and 2 blue balls. If one ball is drawn and not replaced, what is the probability of drawing a red ball first and then a blue ball ? A student has a 70% chance of passing Math and a 60% chance of passing English. What is the probability that the student passes both subjects ?

18. In a deck of 52 cards, what is the probability of drawing an Ace and then drawing a King without replacement? A jar contains 4 chocolate cookies and 6 vanilla cookies. If one cookie is taken out and not replaced, what is the probability of first drawing a chocolate cookie and then a vanilla cookie?

19. Thank you!