Probability of an Event

The following sample space could belong to which of the following scenarios?
Green, Red, Blue
Green, Blue, Red
Blue, Red, Green
Blue, Green, Red
Red, Green, Blue
Red, Blue, Green

• Randomly picking 3 marbles out of a bag with 3 colors and 5 marbles.
• Randomly picking 3 marbles out of a bag with 3 colors and 3 marbles.
• Randomly picking 3 marbles out of a bag with 5 colors and any number of marbles.
• Randomly picking any number of marbles out of a bag with 3 colors and any number of marbles.

Which of the following represents the sample space of flipping a coin 3 times?

• TTT, HHH
• TTT, HHH, THT, HTH, TTH
• HH, TT, TH, HT
• HHH, TTT, THT, THH, TTH, HTH, HTT, HHT

An even "A" will occur with probability 0.7. An event "B" will occur with probability 0.4. The probability that both will occur is 0.2.

Which of the following is true regarding independence between events A and B?

• Events A and B are independent because P(A∩B) = P(A)

• Events A and B are not independent events because P(A∩B) ≠ P(A)

• Events A and B are independent events because P(A∩B)/P(B) = P(A)

• Events A and B are not independent events because P(A∩B)/P(B) ≠ P(A)

Above is a two-way table listing the class and surviving data from the Titanic that sank in 1912.
Are the events "First Class" and "surviving" independent? What does this say about the classes and surviving the accident?

• The events first class and surviving are independent.
  This means that surviving the accident may have been dependent on what class you were in.
• The events first class and surviving are NOT independent.
  This means that surviving the accident may have been dependent on what class you were in.
• The events first class and surviving are NOT independent.
  This means that surviving the accident may NOT have been dependent on what class you were in.
• The events first class and surviving are independent.
  This means that surviving the accident may NOT have been dependent on what class you were in.

Above is a two-way table listing the subjects and passing total for a particular high school.
Using the two-way table, how many students passed math, did not pass English, and took science?

• 271 passed math, 56 did not pass English, and 276 took science.
• 375 passed math, 369 did not pass English, and 1076 took science.
• 271 passed math, 56 did not pass English, and 128 took science.
• 419 passed math, 56 did not pass English, and 276 took science.

Above is a two-way table listing the class and surviving data from the Titanic that sank in 1912.

Which of the following is the correct number that would fill in "Second Class" and "survived"?

• 1,287

• 119

• 117

• 289

Above is a two-way table listing the subjects and passing for a particular high school.
What is the proportion (percentage) of students that are in English, given that they passed a class?

• 369/768
• 369/425
• 369/1076
• 425/768

An event "A" will occur with a probability 0.7. An event B will occur with probability 0.4. The probability that both A and B occur is 0.2. What is the conditional probability of A given B?

• 0.57
• 0.29
• 1.00
• 0.50

The probability of a randomly selected American adult having a career paying more than $100,000 is 20%. The proportion of American adults with a Master's Degree (more than 4 years of college) is 30%.
What is the probability of randomly selecting a person with a Master's Degree and making more than $100,000?

• 0.06
• 0.50
• 0.94
• 0.10

The probability of event A is 0.43, the probability of event B is 0.32, and the probability of event C is 0.66. What is the probability of all three events occurring at the same time?

• 1.4100
• 0.9092
• 0.0908
• 0.6547