Lesson 11.8 – 11.9 Compound Probability Essential Question: How do you find compound probability?

Before we start… Suppose you randomly select a classmate. Event A is selecting a female student and event B is selecting a student with brown eyes. Can these events occur at the same time?

What is a compound event? A compound event combines two or more events, using the word and or the word or.

How do you find P(A or B)? To find the probability that either event A or event B occurs, determine how the events are related first. Mutually exclusive events Overlapping events

What is a mutually exclusive event? A mutually exclusive event or disjoint event has no common outcomes. Event A: Roll a 3. Event B: Roll an even number. 𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃(𝐵)

What is an overlapping event? Event A: Roll an odd number. Event B: Roll a prime number. An overlapping event has at least one outcome in common. 𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃(𝐴 and 𝐵)

You roll a number cube. Find the probability that you roll a number less than 4 or roll a 5.

Fifty tickets are sold for a raffle Fifty tickets are sold for a raffle. You buy 2 tickets, and your friend buys 3 tickets. One ticket is randomly chosen as the winning ticket. What is the probability that you or your friend wins the raffle?

You draw a card from a bag that contains 4 yellow cards numbered 1 – 4 and 5 blue cards numbered 1 – 5. Find the probability that you choose a card with an even number or you choose a number 4 card. 1 1

You draw a card from a bag that contains 4 yellow cards numbered 1 – 4 and 5 blue cards numbered 1 – 5. Find the probability that you choose a yellow card or you choose a number 5 card. 1 1

How do you find P(A and B)? To find the probability that either event A and event B both occur, determine how the events are related first. Independent events Dependent events

What is an independent event? Two events are independent events if the occurrence of one event has no effect on the occurrence of the other. 𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵)

What is a dependent event? Two events are dependent events if the occurrence of one event affects the occurrence of the other. 𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵 given 𝐴)

Carnival Tara is playing a game at a carnival where she picks a rubber duck from a pond. There are 12 ducks in the pond for which there is no prize and 4 ducks that will award a prize. What is the probability that Tara picks a prize-winning duck, replaces the duck in the pond, then picks another prize-winning duck?

A computer randomly generates 4-digit passwords A computer randomly generates 4-digit passwords. Each digit can be used more than once. What is the probability that the first two digits in your password are both 1?

Game Show On a game show, you spin the wheel at the right Game Show On a game show, you spin the wheel at the right. It is divided into equal sections. Find the probability that you get $200 on your first spin and go bankrupt on your second spin.

A box contains 3 blue pens and 5 black pens A box contains 3 blue pens and 5 black pens. You choose one pen at random, do not replace it, then choose a second pen at random. What is the probability that both pens are blue?

A bag contains 4 red, 5 green and 2 blue marbles A bag contains 4 red, 5 green and 2 blue marbles. You randomly draw one marble, don’t replace it, and then draw a second marble. What is the probability that both are red?

A vase holds 7 red roses and 5 pink roses A vase holds 7 red roses and 5 pink roses. You randomly choose a rose, place it in a different vase, then randomly choose another rose. What is the probability that both the first and second roses are red?

Compound Probability To find P(A or B) when… …use this formula events A and B have no common outcomes 𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃(𝐵) events A and B have at least one common outcome 𝑃 𝐴 or 𝐵 =𝑃 𝐴 +𝑃 𝐵 −𝑃(𝐴 and 𝐵) To find P(A and B) when… events A and B are independent 𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵) events A and B are dependent 𝑃 𝐴 and 𝐵 =𝑃(𝐴)∙𝑃(𝐵 given 𝐴)

How do you find compound probability?

Ticket Out the Door A group of students consists of 6 girls and 7 boys. Two students are chosen at random one at a time. What is the probability that both students who are selected are girls?