All Free Statistics MCQs with Answers

• A. 1/3
• B. 2/3
• C. 1/2
• D. 0

Explanation: Let P(T)=p, so P(H)=2p. Since P(H)+P(T)=1, 3p=1 and therefore P(H)=2/3.

• A. 4/5
• B. 1/20
• C. 0
• D. 1/9

Explanation: Using P(A|B)=P(A∩B)/P(B), we get 1/4=(1/5)/P(B). Rearranging gives P(B)=4/5.

• A. 1/4
• B. 2/4
• C. 3/4
• D. 4/4

Explanation: With two fair coins, the four equally likely outcomes are HH, HT, TH, and TT. Three contain at least one head, so the probability is 3/4.

• A. 1/8
• B. 2/8
• C. 5/8
• D. 7/8

Explanation: Only one outcome, tails-tails-tails, gives exactly three tails. With three fair coins there are 2^3 = 8 equally likely outcomes, so the…

• A. 18/36
• B. 9/36
• C. 6/36
• D. 12/36

Explanation: A sum of two dice is odd when one die shows an odd number and the other an even number.

• A. 7/12
• B. 6/12
• C. 12/12
• D. 4/12

Explanation: The probability is favourable outcomes divided by total outcomes. Six white balls out of 12 balls give 6/12, which can also be simplified…

• A. 1/6
• B. 2/6
• C. 3/6
• D. 6/6

Explanation: The even outcomes on a die are 2, 4, and 6, giving three favourable outcomes out of six. Therefore the probability is 3/6, or 1/2.

• A. 13/52
• B. 12/52
• C. 16/52
• D. 3/52

Explanation: Picture cards are jacks, queens, and kings: 3 ranks in each of 4 suits, making 12 cards.

• A. Positive
• B. Zero
• C. None of these
• D. Negative

Explanation: Probability ranges from 0 to 1, so it may be zero but cannot be negative. A negative value has no meaning as an event probability.

• A. Appeared
• B. Exactly
• C. Space
• D. Elementary event

Explanation: An elementary event contains exactly one sample point, such as obtaining a six when rolling a die.

• A. 16
• B. 24
• C. 12
• D. Non of these

Explanation: In a standard 52-card deck, the picture cards are the jacks, queens, and kings in four suits, so there are 3 × 4 = 12.

• A. Dependent events
• B. Independent events
• C. Equally likely events
• D. Mutually Exclusive events

Explanation: Independent events occur without changing each other’s probabilities, so the occurrence of one does not affect the other.

• A. Equally likely events
• B. Exhaustive events
• C. Mutually Exhaustive events
• D. dependent events

Explanation: Events with equal chances of occurring are called equally likely events.

• A. As any other
• B. both event occurs
• C. One occurs
• D. not both occurs

Explanation: Equally likely events have the same probability as one another, so each occurs with the same chance as any other event under…

• A. Sample point
• B. Set
• C. Event
• D. Space

Explanation: An event is any subset of the sample space, including a single outcome or several outcomes.

• A. Probability
• B. Event
• C. Random Variable
• D. Z-Value
• E. Random Experiment

Explanation: An event is a collection of one or more outcomes from a random experiment.

• A. Independent events
• B. Mutually Exclusive events
• C. Bayesian
• D. Empirical

Explanation: The special addition rule applies when events are mutually exclusive, so they cannot occur together and their probabilities are added…

• A. The likelihood of two events happening together
• B. The likelihood of two events happening given that another event has already ha
• C. Based on two mutually exclusive events
• D. Also called Prior probability

Explanation: Joint probability measures the chance that two events occur together, written as P(A∩B).

• A. 4/52
• B. 1/26
• C. 8/52
• D. 1/169

Explanation: There are four fives and four sevens, giving 8 favourable cards out of 52.

• A. Classical Probability
• B. Subjective Probability
• C. Relative Frequency
• D. Independent

Explanation: Classical probability assumes that all outcomes are equally likely, such as the outcomes of a fair die.