Basic Rules of Probability

What is the formula to calculate the probability of the union of two events A and B?

• P(A ∪ B) = P(A) - P(B)

• P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

• P(A ∪ B) = P(A) * P(B)

• P(A ∪ B) = P(A) / P(B)

Tags

CCSS.HSS.CP.B.7

Find P(X⋃Y) if P(X)=0.6, P(Y)=0.4 and P(X⋂Y)=0.2.

• 0.4

• 0.8

• 0.2

• 0.1

Answer explanation

To find P(X⋃Y), use the formula P(X⋃Y) = P(X) + P(Y) - P(X⋂Y) = 0.6 + 0.4 - 0.2 = 0.8. Therefore, the correct answer is 0.8.

Tags

CCSS.HSS.CP.B.7

If P(A)=0.3, P(B)=0.5 and P(A∪B)=0.7, what is P(A ∩ B)?

• 0.1

• 0.2

• 0.4

• 0.9

Answer explanation

To find P(A ∩ B), use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Substituting the given values, 0.7 = 0.3 + 0.5 - P(A ∩ B), solving gives P(A ∩ B) = 0.1.

Tags

CCSS.HSS.CP.B.7

If P(A)=0.7, P(B)=0.6 and P(A⋂B)=0.5, what is the P(A'⋂B')?

• 0.6

• 0.4

• 0.1

• 0.2

Answer explanation

To find P(A'⋂B'), we use the formula P(A'⋂B') = 1 - P(A⋃B) = 1 - (P(A) + P(B) - P(A⋂B)) = 1 - (0.7 + 0.6 - 0.5) = 0.2

What does it mean for two events A and B to be mutually exclusive?

• They cannot occur together

• They always occur together

• One event affects the other

• They do not affect each other's probabilities

Answer explanation

Two events A and B are mutually exclusive if they cannot occur together, meaning the occurrence of one event excludes the possibility of the other event happening.

Tags

CCSS.HSS.CP.A.1

Given P(A)=0.4 and P(B)=0.3. Find P(A⋃B) if A and B are mutually exclusive events.

• 0.1

• 0.12

• 0.7

• 0.75

Answer explanation

Since A and B are mutually exclusive, P(A⋃B) = P(A) + P(B) = 0.4 + 0.3 = 0.7. Therefore, the correct answer is 0.7.

Tags

CCSS.HSS.CP.B.7

In a group of students, 60% like Mathematics, 40% like Accounting and 20% like both subjects. What is the probability that a randomly chosen student likes only one of the subjects?

• 0.2

• 0.4

• 0.6

• 0.8

Answer explanation

The probability of liking only one subject is the sum of those who like Math only (60%-20%=40%) and Accounting only (40%-20%=20%), which equals 60% (40%+20%). So the answer is 0.6.

Tags

CCSS.HSS.CP.B.7

A fair die is rolled. Let event A be rolling an odd number, and event B be rolling a number greater than 2. What is P(A∩B)?

Answer explanation

Sample space when rolling a die, S={1,2,3,4,5,6}, so n(S)=6.

Rolling an odd number, A={1,3,5}

Rolling a number greater than 2, B={3,4,5,6}

Then, the intersection (same elements) of A and B is {3,5}.

So, the probability is 2/6 which can be simplified to 1/3.

In a bag, there are 5 red balls and 3 green balls. If you draw two balls one by one without replacement, what is the probability of drawing at least one red ball?

Answer explanation

To find the probability of drawing at least one red ball, calculate the probability of not drawing any red balls (drawing both green balls) and subtract from 1.

Probability = 1 - (3/8 * 2/7) = 25/28.

You have two urns. In the first urn, there are 4 red balls and 3 blue balls. In the second urn, there are 2 red balls and 5 blue balls. A ball is randomly chosen from the first urn then put into the second urn. Then another ball is taken from the second urn. What is the probability of choosing the same color of balls from the first urn and the second urn?

Answer explanation

If the first red ball is taken from the first urn (4 red balls, 3 blue balls) and then put into the second urn, the number of balls in the second urn will increase by 1 that is 3 red balls and 5 blue balls. So, the probability of choosing both red balls is 4/7*3/8=3/14.

If the first blue ball is taken from the first urn (4 red balls, 3 blue balls) and then put into the second urn, the number of balls in the second urn will increase by 1 that is 2 red balls and 6 blue balls. So, the probability of choosing both blue balls is 3/7*6/8=9/28.

So, total probability of choosing the same color of balls is 3/14+9/28=15/28.