2.1PROBABILITY OF UNION OF TWO EVENTS.pptx

PPT on Q4 math 10

1. Illustrate the Probability of a Union of Two Events DEBBIE ANN LAOGAN PRE-SERVICE TEACHER

2. OBJECTIVES At the end of the session, at least 80% of the students should be able to: Illustrate the probability of a union of two events - Mutually exclusive and Non-Mutually exclusive events; Find the probability of a union of two events - Mutually exclusive and Non-Mutually exclusive events; and Engage in hands-on and group activities to simulate and experiment with the probability of a union of two events.

3. FIND ME! (CHECKING OF ASSIGNMENT)

4. ______a. A king or an ace? ______b. A number card or an ace? ______c. A black card or a diamond? ______d. A number 3 or a heart? ______e. A black card or 10 of spades? ______f. A face card or a diamond? A card is drawn at random from a 52 – deck of cards. Find the Probability of getting:

5. A card is drawn at random from a 52 – deck of cards. Find the Probability of getting: a. A king or an ace? b. A number card or an ace? c. A black card or a diamond? d. A number 3 or a heart? e. A black card or 10 of spades? f. A face card or a diamond?  

6. Renz rolled a fair die and wished to find the probability that “the number that turns up is odd or even”.   2.“the number that will turn is even or greater than 3”.

7. PROBABILITY OF THE UNION OF: Mutually exclusive events - are those events that do not occur at the same time. In other words, mutually exclusive events are called disjoint events . If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero. P(A and B) = 0 “ The probability of A and B together equals 0 ”impossible”

8. If two events, A and B, are mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities. In symbols, P(A or B) = P(A) + P(B) or P(A  B) = P(A) + P(B)

9. Non-mutually exclusive events – are events that can happen at the same time. In other words, non-mutually exclusive events are called joint events. The probability of the union of two events A and B  written as P(A  B) or P(A or B)  is equal the to sum of the probability of event A  P(A)  and the probability of event B  P(B)  minus the probability of event A and B occurring together  P(A  B)  . In symbols, P(A  B) = P(A) + P(B) – P(A  B)

10. Renz rolled a fair die and wished to find the probability that “the number that turns up is odd or even”.   Given: S =  1,2,3,4,5,6  A =  1,3,5  B =  2,4,6  Formula: P(A  B) = P(A) + P(B) Solution: P(A  B) =  

11. Renz rolled a fair die and wished to find the probability that 2 .“the number that will turn is even or greater than 3”. Given: S =  1,2,3,4,5,6  A =  2,4,5  B =  4,5,6  (A  B) =  4,6  Formula: P(A  B) = P(A) + P(B) – P(A  B) Solution: P(A  B) =  

12. A pair of dice is rolled. What is the probability that the two dice show the same number or that the sum of the numbers is less than 7?

13. A pair of dice is rolled. What is the probability that the two dice show the same number or that the sum of the numbers is less than 7? Given: A =  1-1,2-2,3-3,4-4,5-5,6-6  B = 1-1,1-2,1-3,1-4,1-5,2-1,2-2,2-3,2-4,3-1,3-2,3-3,4-1,4-2 ,5-1  (A  B) =  1-1,2-2,3-3  Formula: P(A  B) = P(A) + P(B) – P(A  B) Solution: P(A  B) =  

14. A pair of dice is rolled. What is the probability that the two dice show the same number or that the sum of the numbers is less than 8?

15. A pair of dice is rolled. What is the probability that the two dice show the same number or that the sum of the numbers is less than 8? Given: A =  1-1,2-2,3-3,4-4,5-5,6-6  B = 1-1,1-2,1-3,1-4,1-5,1-6,2-1,2-2,2-3,2-4,2-5,3-1,3-2,3-3,3-4,4-1,4-2 ,4-3,5-1,5-2,6-1  (A  B) =  1-1,2-2,3-3  Formula: P(A  B) = P(A) + P(B) – P(A  B) Solution: P(A  B) =  

16.   THINK-PAIR-SHARE

17. A pair of dice is rolled. What is the probability that the two dice show the same number or that the sum of the numbers is less than 5?

18. A pair of dice is rolled. What is the probability that the two dice show the same number or that the sum of the numbers is less than 5? Given: A =  1-1,2-2,3-3,4-4,5-5,6-6  B = 1-1,1-2,1-3,2-1,2-2,3-1 (A  B) =  1-1,2-2  Formula: P(A  B) = P(A) + P(B) – P(A  B) Solution: P(A  B) =  

19. Can you cite an instance in your day-to-day activities applying the probability of union of two events?  At home  In school

20. LET’S SUM IT UP! In solving the probability of the union of two events, if the two sets do not have elements in common, use Mutually exclusive events P(A or B) = P(A) + P(B) o r P(A  B) = P(A) + P(B)   If the two sets have elements in common, use Non-mutually exclusive events P(A or B) = P(A) + P(B) – P(A  B)

21. IT’S YOUR TURN! In one half crosswise sheet of paper, solve the following problem completely. Show complete solution. 5 points each.

22. Simon rolled a fair die and wished to find the probability that “the number that will turn is odd or greater than 4”.   2. If a card is drawn at random from a 52-deck of cards. Find the probability of getting a heart or a diamond card.

23. HOME LEARNING TASK Direction: Solve the following completely. A card is drawn at random from a standard deck of cards. What is the probability of drawing a queen or a king? A die is rolled. What is the probability of getting a prime number or an odd number?

24. THANK YOU!