Get out your ISN!

You will be able to find P(A and B) for independent and dependent events.

Today’s Objectives:

33-34 Multiplication Rule of

Independent Events—Two events A and B are independent if the fact that A occurs does not change the probability of B occurring.Dependent Events—When the outcome of the first event changes the probability of the second event occurring.Conditional Probability—The probability that event B occurs knowing that event A already occurred; P(B|A)

TOCWWK

Probability

Big Picture

FoldableOUTSIDE

INSIDE

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Cut along the dotted line to form the tabs.

Dependent & Independent Events

Dependent & Independent Events

Dependent

IndependentDependent

Dependent

Dependent & Independent EventsDependent OR Independent?You accidently dropped a coin from the top of 10 stairs. What is the probability that it will land on the eighth step, tails up?

.What is your first event? ________________________________________

.Second? ________________________________________

.If the coin does land on the eighth step, does that change the probability that it will land tails up? ______________________________

ANSWER: ________________________

Landing on the 8th step

Tails up

noIndependent

Extra PracticeThere are 3 black cats and 5 grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black?

Event A =Event B =

THINK: If the first cat to escape is a black cat, does that change the probability that the second will be a black cat?

Black CatBlack Cat

INDEPENDENT? DEPENDENT?

Conditional Probability

probabilityof B given A

Conditional Probability

Jack AceJackAce

I drew a Jack and now I want to draw an Ace. How many Aces and cards are left in the deck?

¿𝒐𝒇 𝒂𝒄𝒆𝒔¿𝒐𝒇 𝒄𝒂𝒓𝒅𝒔𝒊𝒏𝒅𝒆𝒄𝒌

=𝟒𝟓𝟏

Conditional Probability

7 >4>4 7

I drew a 7 and now I want to draw a number >4. Howmany numbers >4 and total numbers are left in the hat?

¿ 𝒔❑′ >𝟒 𝒊𝒏𝒉𝒂𝒕

𝒂𝒍𝒍 ¿′ 𝒔𝒊𝒏𝒅𝒆𝒄𝒌=𝟓𝟗

Multiplication Rule of Probability

P(A and B)

P(A)*P(B)

P(A)*P(B|A)

Multiplication Rule of Probability

P(A and B)

spade spade

P(A and B)

Annie JustinYES, Dependent

P(A and B)

P(A and B)

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11/24 RightSide Input

Multiplication Rule of Probability

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11/24 LeftSide Input

Multiplication Rule of Probability

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