Free Probability MCQs with Answers

• 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.

• 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…

• 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…

• 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.

• 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.

• 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.

• A. 5
• B. 5×5
• C. 1
• D. None of these

Explanation: Choosing all 5 objects from 5 gives only one possible selection, so \(\binom{5}{5}=5!/(5!0!)=1\).

• 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.

• 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.