13-4 Probability of Compound

Events

Probability of two independent events A and B.P(A and B)=P(A)*P(B)

1)Using a standard deck of playing cards, find the probability of drawing a king, replacing it, then drawing a second king.

2)Find the probability of rolling a sum of 7 on the first toss of two dice and a sum of 4 on the second toss.

3) The probability of your grandma getting arthritis is 1/5. Additionally, the probably she’ll fall and break her hip is 1/15. Assuming these two are unrelated, what is the probability grandma will have both?

Probability of Two Dependent Events A and BP(A and B)=P(A)*P(B following A)

1)Using a standard deck of playing cards, find the probability of drawing a king, NOT replacing it, then drawing a second king.

4)What is the probability of randomly selecting two navy socks from a drawer that contains 6 black and 4 navy socks?

• Probability of Two Mutually Exclusive EventsP(A or B) = P(A) + P(B)Mutually Exclusive: Two events that can not happen at the same time

(keyword:”or”)

Examples:• Turning left and turning right are Mutually Exclusive

(you can't do both at the same time)• Tossing a coin: Heads and Tails are Mutually Exclusive• Cards: Kings and Aces are Mutually Exclusive

What is not Mutually Exclusive:• Turning left and scratching your head can happen at

the same time• Kings and Hearts, because you can have a King of

Heart

5)You are a contestant in a game where if you select a blue ball or red ball you get a million dollars. You must select the ball at random from a box containing 2 blue, 3 red, 9 yellow, and 10 green balls. What is the probability that you will win the money?

6)What is the probability of picking 5 male puppies of which you want at least 3 to be male, from a group of 9 that contains 5 males and 4 females

Probability of Inclusive EventsP(A or B) = P(A) + P(B) – P(A and B)

Inclusive Events: Events that are not mutually exclusive and can overlap(can happen at the same time!)

FYI: Sometimes we use symbols for the words “and” and “or”

• P(A or B) = P(A) + P(B) - P(A and B)

• Here is the same formula, but using ∪ and ∩:• P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

7)What is the probability that when you pick a card from a deck it is either black or a jack?

8)The weatherman says the probability of rain is 2/5, lighting is 3/5, and both is 1/5. What is the probability the baseball game will be cancel due to either rain or lighting?

10)The probability for a student to pass the road test for their license the first time is 5/6. The probability of passing the written part on the first attempt is 9/10. The probability of passing both the road and written tests on the first attempt is 4/5. Are these events mutually exclusive or mutually inclusive?

• What is the probability that you can pass either part on the first attempt?o P(Passing road)=o P(Passing written)=o P(Passing both)=

o P(Passing either)=