5.3 Conditional Probability and Independence

​Conditional probability is the likelihood of an event occurring, given that another event has already occurred. It is written as P(A|B), meaning the probability of event A happening given that event B has already happened.
Mutually exclusive events are events that cannot happen at the same time. The probability of two mutually exclusive events, A and B, occurring simultaneously is zero: P(A and B) = 0.

Not mutually exclusive events, also called inclusive events, are events that can occur at the same time because they have overlapping outcomes.

Multiple Choice

Marti rolls two dice. What is the probability that the sum of the dice is equal to 7, given that the first die is showing a 2? Write as a simplified fraction using "/".

• 1/6
• 1/12

• 2/3

• 1/2

Multiple Choice

What is the probability a passenger on the Titanic surviving given they are in first class?

• .2855

• .6246

• .0922

• .3230

Open Ended

Are the events "male" and "left-handed" independent? Justify your answer.

Multiple Choice

A bottle contains 1 green and 1 red ball. A ball is drawn at random, replaced in the bottle and another ball is drawn. Find the sample space from the tree diagram shown.

• GR, RG, RR

• GG, RR

• GG, GR, RR

• GG, GR, RG, RR

Multiple Choice

What is the formula for finding the probability that events A and B both occur?

• P(A ∩ B) = P(A) + P(B | A)

• P(A ∩ B) = P(A) • P(B | A)

• P(A ∩ B) = P(A) - P(B | A)

• P(A ∩ B) = P(A) / P(B | A)

Multiple Choice

Use the tree diagram to find the probability of tossing a head first and then a tail when a coin is tossed twice.

• 1

• 1_/2

• 1/₄

• 1/8

Multiple Choice

What is the multiplication rule for independent events?

• P(A ∩ B) = P(A) + P(B)

• P(A ∩ B) = P(A) • P(B)

• P(A ∩ B) = P(A) - P(B)

• P(A ∩ B) = P(A) / P(B)

Multiple Choice

A game is played where a fair coin is flipped.

Heads you lose, tails you get to flip again.

On the second go heads you lose and tails you win.

What is the probability of winning?

• ¹/₂

• ¹/₄

• ³/₄

• 1

Multiple Choice

What will we learn about in the next chapter regarding random variables?

• Discrete and Continuous Random Variables

• Transforming and Combining Random Variables

• Binomial and Geometric Random Variables

• All of the above

Dropdown

FIRST BLANK

Select answer

SECOND BLANK ​ ​ ​

Select answer

Match

A school requires students to wear uniforms. They can choose from the following options.

• How many total choices does a student have?

• What is the probability of choosing a gray hoodie, navy polo and khaki pants?

• What is the probability of choosing a black polo?

16

1/16

1/4

• 16

• 1/16

• 1/4

Multiple Choice

If you are picking a card randomly from a deck of cards, the events of picking a jack and picking a heart are mutually exclusive.

• True

• False

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a 5 or a diamond?

• 2/52
• 4/52
• 16/52
• 26/52

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a spade or a red card?

• 13/52
• 26/52
• 39/52
• Not possible

Multiple Choice

If events A and B are mutually exclusive, what is P(A and B)?

• 0.50

• 0

• 1

• 0.75

Multiple Choice

• No.

• Yes.

• Maybe.

• I dont know.

Multiple Choice

If a student is chosen at random, find the probability of getting someone who is a regular or heavy smoker. Round your answer to three decimal places.

• 0.221

• 0.662

• 0.193

• 0.128

Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident