Probability Q&A

Definition

100

What does the symbol U represent?

Union "or"

200

These are events that cannot happen at the same time.

Mutually Exclusive Events

300

These are events where the outcome of one event influences or affects the probability of the outcome of another event.

Dependent Events

400

It is the set of all outcomes that are NOT in the event.

Complement

500

It is a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle, common elements of the sets being represented by the areas of overlap among the circles.

Venn Diagram

Formula

100

What is the formula for Mutually Exclusive Events?

P(AUB) = P(A) + P(B)

200

What is the formula for Independent Events?

P(A ∩ B) = P(A) * P(B)

300

What is the formula for Not-Mutually Exclusive Events?

P(AUB) = P(A) + P(B) - P(A∩B)

400

What is the formula for Dependent Events?

P(A ∩ B) = P(A) * P(B following A)

500

What is the formula for Conditional Probability?

P(A|B) = P(A and B) / P(B) 

Union / Intersection

100

If A = {red, green, blue}

B = {red, yellow, orange}

C = {red, orange, yellow, green, blue, purple}

Find: A U B

{red, green, blue, yellow, orange}

200

If A = {red, green, blue}

B = {red, yellow, orange}

C = {red, orange, yellow, green, blue, purple}

Find: A ∩ B

{red}

300

If A = {red, green, blue}

B = {red, yellow, orange}

C = {red, orange, yellow, green, blue, purple}

Find: A ∩ C

{red, green, blue}

400

If A = {red, green, blue}

B = {red, yellow, orange}

C = {red, orange, yellow, green, blue, purple}

Find: A U C

{red, green, blue, orange, yellow, purple}

500

If A = {red, green, blue}

B = {red, yellow, orange}

C = {red, orange, yellow, green, blue, purple}

Find: (A U B) ∩ (A U C)

{red, green, blue, yellow, orange}

And / Or

100

A survey of 100 people shows that 60 own a cat, 40 own a dog, and 20 own both cat and dog. How many people own either a cat or a dog?

80

200

If the probability of event A occurring is 0.6 and the probability of event B occurring is 0.4, and they are mutually exclusive, what is the probability of either A or B occurring?

1

300

What is the probability that a card drawn from a standard deck is either a king or a heart?

4/13

400

In a cafeteria, 70% of students choose burger, 50% choose salad, and 20% choose both. What is the probability that a student chooses burger or salad?

100%

500

A survey shows 60% of people like chocolate ice cream and 40% like strawberry, and 20% like both. What percentage of people like chocolate or strawberry ice cream?

80%

Conditional

100

In a certain city, 60% of people prefer coffee, and 40% prefer tea. 20% of the coffee drinkers also prefer tea. What is the probability that a person prefers coffee given that they prefer tea?

0.50

200

A student takes two tests. The probability of passing the first test is 0.80, and the probability of passing the second test is 0.70. The probability of passing both tests is 0.60. What is the probability that the student passes the second test given that they passed the first test? 

0.75

300

A drawer contains 10 black socks and 7 white socks. Two socks are drawn at random without replacement. What is the probability that the second sock is black given that the first sock was black?

9/16

400

Two dice are rolled. What is the probability that the sum is 7 given that at least one die shows a 3?

2/11

500

A card is drawn at random from a standard deck of 52 cards. What is the probability that the card drawn is an ace, given that it is a spade?

1/13