All Free Statistics MCQs with Answers
Every Statistics question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.
545 questions · page 48 of 55
471. Discrete random variable is real valued function defined on a ___________ sample space?
- A. Discrete
- B. Variable
- C. Scale
- D. Non of these
Explanation: A discrete random variable is defined on a discrete sample space, whose outcomes can be listed or counted. This distinguishes it from a continuous random variable associated with an interval of possible values.
Correct answer: Discrete472. Sum of dots when two dice are rolled is____________?
- A. a discrete variable
- B. a continuous variable
- C. a constant
- D. a qualitative variable
Explanation: The sum of two dice can take only the integer values 2 through 12, giving a finite set of possible outcomes. A variable with countable possible values is discrete, not continuous.
Correct answer: a discrete variable473. If A and B are mutually exclusive then?
- A. P(AorB) =0
- B. P(AandB)=0
- C. P(AnorB)=0
- D. P(AeitherB)=0
Explanation: Mutually exclusive events cannot occur together, so their intersection is empty and P(A and B) equals zero. Their union need not be zero because either event may still occur.
Correct answer: P(AandB)=0474. Two mutually exclusive events are __________?
- A. Dependent
- B. Independent
- C. Overlapped
- D. None of These
Explanation: Mutually exclusive events cannot occur together, whereas independent events can occur together without affecting each other, so mutually exclusive events are conventionally described as dependent. This assumes both events have positive probability.
Correct answer: Dependent475. Which of the following is not a correct statement about a Probability _________________?
- A. It must have a value between 0 and 1
- B. It can be reported as a decimal or a fraction
- C. A value near 0 means that the event is not likely to occur/happens
- D. It is the collection of several experiment
Explanation: A probability is a numerical measure between 0 and 1 and may be written as a decimal or fraction; a value near 0 indicates an unlikely event. A collection of experiments is not a probability, but may be called a sample space or experiment set depending on context.
Correct answer: It is the collection of several experiment476. The special rule of multiplication of probability, the events must be ______________?
- A. Independent
- B. Mutually exclusive
- C. Bayesian
- D. Empirical
Explanation: The special multiplication rule, P(A∩B) = P(A)P(B), applies when events are independent. Mutually exclusive events cannot occur together, which is a different relationship and generally gives an intersection probability of zero.
Correct answer: Independent477. if you roll a pair of dice, what is the probability that (at least) one of the dice is a 4 or the sum of the dice is 7 ?
- A. 4/36
- B. 13/36
- C. 21/36
- D. 15/36
Explanation: There are 11 outcomes with at least one 4 and 6 outcomes whose sum is 7; 2 outcomes belong to both groups. Thus the union has 11 + 6 − 2 = 15 outcomes out of 36, giving 15/36.
Correct answer: 15/36478. . If the occurrence of one event means that another cannot happen, then the events are _______________?
- A. Independent
- B. Mutually Exclusive
- C. Bayesian
- D. Empirical
Explanation: If occurrence of one event rules out the occurrence of another, their intersection is empty, so they are mutually exclusive. Independent events may occur together, so independence does not fit this description.
Correct answer: Mutually Exclusive479. 5C5 is equal to ________________?
- A. 5
- B. 5×5
- C. 1
- D. None of these
Explanation: Choosing all 5 objects from 5 gives only one possible selection, so \(\binom{5}{5}=5!/(5!0!)=1\).
Correct answer: 1480. The product of first 'n' natural numbers is _____________?
- A. 1.2.3.4,.........
- B. 1.2.3......(n-2) (n-1) (n)
- C. n. (n-1) (n-2)..............3.2.1.0
- D. None of these
Explanation: The product of the first n natural numbers is 1 × 2 × 3 × ⋯ × n, which is written as n!. Option b expresses this product in ascending order.
Correct answer: 1.2.3......(n-2) (n-1) (n)