G10 Math Q3- Week 7- Probability of Union of Two Events.ppt
- 9. Finding Outcomes of more than one event • The total outcomes of each event are found by using a tree diagram or by using the fundamental counting principle. • Example: At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey, or ham, and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.
- 10. Probability of Compound Events • A compound event consists of two or more simple events. • Examples: rolling a die and tossing a penny spinning a spinner and drawing a card tossing two dice tossing two coins
- 11. Probability of Compound Events Example: List down the following events for the coin-die experiment. 1. The event A in which the coin comes up Heads(H)
- 12. Probability of Compound Events Example: List down the following events for the coin-die experiment. 2. The event B in which the coin comes up Tails(T)
- 13. Probability of Compound Events Example: List down the following events for the coin-die experiment. 3. The event C comes up 1.
- 14. Probability of Compound Events Example: List down the following events for the coin-die experiment. 4. The event D comes up 5.
- 15. Probability of Compound Events Example: List down the following events for the coin-die experiment. 5. The event F in which die does not come up 6.
- 16. Probability of Compound Events Example: List down the following events for the coin-die experiment. 6. The event H in which the coin comes up Heads and the die, a number greater than 3.
- 17. Probability of Compound Events Example: List down the following events for the coin-die experiment. 7. The event I in which the coin comes up Tails and the die, an even number.
- 18. Probability of Compound Events ACTIVITY: 1. Four coins are tossed. List down the elements of the following events. A= Four Heads B= Three Heads and one Tail
- 19. Probability of Compound Events ACTIVITY: 2. A card is selected from an ordinary deck of playing cards ( 52 pieces). Name the elements in each of the given events. A= the card selected is diamond. B= the card selected is a seven. C= the card selected is a queen. D= the card selected is a King of Hearts.
- 20. Probability of Compound Events ACTIVITY: 2. A card is selected from an ordinary deck of playing cards ( 52 pieces). Name the elements in each of the given events. A= the card selected is diamond. B= the card selected is a seven. C= the card selected is a queen. D= the card selected is a King of Hearts.
- 21. Compound Events • When the outcome of one event does not affect the outcome of a second event, these are called independent events. • The probability of two independent events is found by multiplying the probability of the first event by the probability of the second event.
- 26. Events that cannot occur at the same time are called mutually exclusive. Suppose you want to find the probability of rolling a 2 or a 4 on a die. P(2 or 4) Since a die cannot show both a 2 and a 4 at the same time, the events are mutually exclusive.
- 27. Problem-Solving: 1. Two dice are rolled. What is the probability of getting : a. A 4 or a 6 b. Not 3 or a 5
- 28. Problem-Solving: 2. There are 3 red pens, 4 blue pens, 2 black pens, and 5 green pens in a drawer. Suppose you choose a pen at random. a. What is the probability that the pen chosen is red or blue? b. What is the probability that the pen chosen is blue or green? c. What is the probability that the pen chosen is red or black?
- 29. ACTIVITY:
- 40. Directions: Based form the given pair of events in each item, write ME on the space provided before each number if the outcomes in the events are MUTUALLY EXCLUSIVE or MI if MUTUALLY INCLUSIVE. ____ 1. Choosing a 7 or choosing a diamond in a deck of cards. ____ 2. Choosing a 7 and a jack in a deck of cards. ____ 3. Rolling a number less than 4 or rolling a number greater than 4 in a die. ____ 4. Rolling a 2 or rolling an even number in a die. ____ 5. Rolling a 1 or rolling a prime number in a die. ____ 6. Choosing a day that begins with letter S or choosing a Sunday in a week. ____ 7. Choosing a weekday or choosing a weekend day in a week. ____ 8. Choosing a letter R or choosing a vowel in the alphabet. ____ 9. Choosing a letter E or choosing a letter C in the alphabet. ____ 10. Choosing the month of April or Choosing a summer month in the Philippines. Activity 3: Mutually Exclusive or Not?
- 41. Mutually exclusive 1.Makoy has 60 red chips, 10 yellow chips, and 18 white chips. What is the probability that Makoy randomly selects a red chip or a white chip? 2. A card is drawn from a deck of cards. What is the probability of getting a spade or a queen? NOT MUTUALLY EXCLUSIVE
- 42. Not Mutually exclusive events 3. A box contains 15 chips numbered 1-15. If one chip is drawn from a box, what is the probability of getting a number 2 or an even number?
- 43. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE EVENTS. A. DETERMINE WHETHER THE SITUATION IS MUTUALLY EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS (MI).
- 44. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE EVENTS. A. DETERMINE WHETHER THE SITUATION IS MUTUALLY EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS (MI).
- 45. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE EVENTS. A. DETERMINE WHETHER THE SITUATION IS MUTUALLY EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS (MI).
- 46. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE EVENTS. B. DETERMINE WHETHER THE SITUATION IS MUTUALLY EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS (MI). 1. A restaurant serves a bowl of candies to its customers. The bowl of candies Gabriel receives has 10 chocolate candies, 8 coffee candies, and 12 caramel candies. After Gabriel chooses a candy, he eats it. Find the probability of getting candies with the indicated flavors. a. P (chocolate or coffee) b. P (caramel or coffee) c. P( chocolate or caramel)
- 47. ACTIVITY ON MUTUALLY AND NOT MUTUALLY EXCLUSIVE EVENTS. B. DETERMINE WHETHER THE SITUATION IS MUTUALLY EXCLUSIVE(ME) OR NOT MUTUALLY EXCLUSIVE EVENTS (MI). 2. Rhian likes to wear colored shirts. She has 15 shirts in the closet. Five of these are blue, four shades of red, and the rest are of different colors. What is the probability that she will wear a blue or a red shirt?