13 4 Find the Probability of Compound Events

13 -4 Find the Probability of Compound Events

Compound Event • Combines 2 or more events using AND or OR.

Consider these events… Randomly select a number from 1 to 20. Event A: Select an even number. Event B: Select a number less than 2. 2 4 6 8 10 12 14 16 18 20 o AH AD AS Mutually exclusive events n n o 1 Randomly select a card from 52 card deck. Event A: Select an Ace Event B: Select a Club AC 2 C 3 C 4 C 5 C 7 C 8 C 9 C 10 C JC QC KC no outcomes in common Aka Disjoint events Overlapping events n one or more outcomes in common 6 C

Mutually Exclusive or Overlapping? 2 3 4 1 You draw a card from a bag that contains 4 yellow cards numbered 1 -4 and 4 blue cards numbered 1 -4. Tell whether the events A and B are mutually exclusive or overlapping. 3 mutually exclusive 1 overlapping mutually exclusive 4 overlapping 3 1 overlapping

Event A 1 2 Event B 3 5 6 4 Event A: Roll a number less than 4. Event B: Roll a number greater than 4. Probability of Mutually Exclusive or Disjoint Events

Finding the Probability of Disjoint Events A bag of marbles contains 25 yellow marbles, 40 red marbles, 5 purple marbles, and 30 blue marbles. You randomly draw a marble from the bag. What is the probability that you draw a yellow or a purple marble? Event A: You choose a yellow marble. Event B: You choose a purple marble.

Event A Event B 2 1 3 6 4 5 Event A: Roll a number less than 5. Event B: Roll an even number. Probability of Overlapping Events

Finding the Probability of Overlapping Events You randomly choose a number from 1 to 30. What is the probability that you choose a prime number or a number greater than 20? Event A: You choose a prime number. Event B: The number is greater than 20. Overlap: The number is prime and greater than 20.

• Independent events – Occurrence of one event does not effect the probability of the occurrence of the other event. • Dependent events – Occurrence of one event does effect the probability of the occurrence of the other event.

Identifying Independent and Dependent Events Tell whether the events are independent or dependent. You roll a number cube two times and it shows a 3 each time. independent You randomly draw a number from a hat. Then, without putting the first number back, you randomly draw a second number. dependent

Finding the Probability of Independent Events You roll two number cubes. What is the probability that the first number cube shows a prime number and the second number cube shows a number greater than four? Event A: prime number (2, 3, 5) Event B: number greater than 4 (5, 6)

Finding the Probability of Dependent Events A candy dish contains 2 cinnamon candies, 4 spearmint candies, 7 peppermint candies, and 1 wintergreen candy. You randomly draw a piece of candy, then you randomly draw a second piece of candy without replacing the first piece of candy. What is the probability that both the first and the second pieces of candy drawn form the dish are spearmint? Event A: pick spearmint (4 out of 14) Event B given A: pick spearmint (3 out of 13)

Tell whether the events are independent or dependent. Then find P(A and B). independent

Tell whether the events are independent or dependent. Then find P(A and B). dependent

Tell whether the events are independent or dependent. Then find P(A and B). independent

Tell whether the events are independent or dependent. Then find P(A and B). dependent

Compound Event • Combines 2 or more events using AND or OR.