Two Basic Rules of Probability Quiz
The question sheet
Reveal any answer as you study-
According to the multiplication rule, P(A AND B) equals:
- P(A) − P(B)
- P(A)/P(B)
- P(A) + P(B)
- P(B)P(A|B)
Reveal answer
Answer: P(B)P(A|B)
Source evidence
PDF page 197: If A and B are two events defined on a sample space, then: P(A AND B) = P(B)P(A|B). P(A AND B) This rule may also be written as: P(A|B) = P(B) (The probability of A given B equals the probability of A and B divided by the probability of B.)
-
If A and B are independent, then P(A|B) equals:
- 1
- 0
- P(A)
- P(B)
Reveal answer
Answer: P(A)
Source evidence
PDF page 197: If A and B are independent, then P(A|B) = P(A). Then P(A AND B) = P(A|B)P(B) becomes P(A AND B) = P(A)P(B).
-
For independent events A and B, P(A AND B) becomes:
- P(A)P(B)
- 0
- P(A) + P(B)
- P(A) − P(B)
Reveal answer
Answer: P(A)P(B)
Source evidence
PDF page 197: If A and B are independent, then P(A|B) = P(A). Then P(A AND B) = P(A|B)P(B) becomes P(A AND B) = P(A)P(B).
-
If A and B are mutually exclusive, then P(A AND B) equals:
- 0
- P(A)P(B)
- 1
- 0.5
Reveal answer
Answer: 0
Source evidence
PDF page 197: If A and B are defined on a sample space, then: P(A OR B) = P(A) + P(B) - P(A AND B). If A and B are mutually exclusive, then P(A AND B) = 0. Then P(A OR B) = P(A) + P(B) - P(A AND B) becomes P(A OR
-
For Klaus, P(A)=0.6 and P(B)=0.35 with P(A AND B)=0. What is P(A OR B)?
- 1.0
- 0.21
- 0.95
- 0.05
Reveal answer
Answer: 0.95
Source evidence
PDF page 197: • Therefore, the probability that he chooses either New Zealand or Alaska is P(A OR B) = P(A) + P(B) = 0.6
PDF page 197: + 0.35 = 0.95. Note that the probability that he does not choose to go anywhere on vacation must be 0.05.
-
Why is P(A AND B)=0 in the Klaus vacation problem?
- The trips cost the same
- He dislikes both trips
- He can only afford one vacation
- Both trips are identical
Reveal answer
Answer: He can only afford one vacation
Source evidence
PDF page 197: • P(A AND B) = 0 because Klaus can only afford to take one vacation
-
Carlos: P(A)=0.65 and P(B|A)=0.90. What is P(A AND B)?
- 0.715
- 0.90
- 0.585
- 0.423
Reveal answer
Answer: 0.585
Source evidence
PDF page 197: a. The problem is asking you to find P(A AND B) = P(B AND A). Since P(B|A) = 0.90: P(B AND A) = P(B|A)
PDF page 197: P(A) = (0.90)(0.65) = 0.585
-
For Carlos, what is P(A OR B) if P(A AND B)=0.585?
- 0.715
- 0.65
- 1.30
- 0.585
Reveal answer
Answer: 0.715
Source evidence
PDF page 197: P(A OR B) = P(A) + P(B) - P(A AND B) = 0.65 + 0.65 - 0.585 = 0.715
-
Are Carlos's events A and B independent?
- Yes, because P(A)=P(B)
- Yes, they never overlap
- Cannot be determined
- No, P(B AND A)≠P(B)P(A)
Reveal answer
Answer: No, P(B AND A)≠P(B)P(A)
Source evidence
PDF page 197: c. No, they are not, because P(B AND A) = 0.585.
PDF page 198: 0.423 ≠ 0.585 = P(B AND A)
PDF page 198: So, P(B AND A) is not equal to P(B)P(A).
-
For Carlos, P(B)P(A)=(0.65)(0.65) equals:
- 0.130
- 0.715
- 0.585
- 0.423
Reveal answer
Answer: 0.423
Source evidence
PDF page 198: P(B)P(A) = (0.65)(0.65) = 0.423
-
To be mutually exclusive, P(A AND B) must equal:
- one
- 0.585
- P(A)P(B)
- zero
Reveal answer
Answer: zero
Source evidence
PDF page 198: To be mutually exclusive, P(A AND B) must equal zero.
-
In the swim team of 150, what is P(novice swimmer)?
- 75/150
- 80/150
- 28/150
- 40/150
Reveal answer
Answer: 28/150
Source evidence
PDF page 198: Solution 3.16 28 a. 150
Introductory Statistics
Introductory Statistics by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
Make your own — free
Turn any notes into a game in under a minute. Free to start.