150 practice questions covering Probability, organised into 2 topics.
150 questions include a written explanation.
Pick a topic below, or try the samples first.
A bag holds 6 white balls, 5 black balls and 4 yellow balls, alike apart from colour. One ball is drawn at random. What is the probability that the ball drawn is white or yellow?
A$\frac{11}{15}$
B$\frac{1}{3}$
C$\frac{2}{5}$
D$\frac{2}{3}$
Show answer and explanation
Correct answer: D - $\frac{2}{3}$
The bag holds $6 + 5 + 4 = 15$ equally likely balls, and one ball cannot be both white and yellow, so the two probabilities add: $\frac{6}{15} + \frac{4}{15} = \frac{10}{15} = \frac{2}{3}$. The value $\frac{1}{3}$ is the chance of a black ball. The value $\frac{2}{5}$ counts the white balls alone, and $\frac{11}{15}$ adds the black balls in place of the yellow ones.
Q2
easy
Which of these numbers can never be the probability of an event?
A$0$
B$\frac{3}{7}$
C$-0.2$
D$1$
Show answer and explanation
Correct answer: C - $-0.2$
The probability of an event always lies from $0$ to $1$, both included, so a negative number such as $-0.2$ is impossible. The value $0$ is the probability of an impossible event and $1$ is the probability of a sure event, so both are allowed. The value $\frac{3}{7}$ lies between $0$ and $1$ and is an ordinary probability.
Q3
medium
The events $E_1, E_2, \ldots, E_n$ of a sample space $S$ are said to be exhaustive when which condition holds?
AEach $E_i$ contains exactly one sample point of $S$
B$P(E_1) = P(E_2) = \cdots = P(E_n)$
C$E_1 \cup E_2 \cup \cdots \cup E_n = S$
D$E_i \cap E_j = \phi$ for every pair with $i \neq j$
Exhaustive events together cover the whole sample space, so their union is $S$ and at least one of them is bound to occur. The condition on empty intersections defines mutually exclusive events, and events can be exhaustive while still overlapping. Events with one sample point each are elementary events, and equal probabilities describe equally likely events.
Q4
easy
Following the axioms of probability, which statement holds for every event $E$ of a sample space $S$?
A$P(E) > 0$
B$0 \leq P(E) \leq 1$
C$P(E) \geq 1$
D$P(E)$ may be any real number
Show answer and explanation
Correct answer: B - $0 \leq P(E) \leq 1$
The axioms demand $P(E) \geq 0$ for every event together with $P(S) = 1$, and since $E$ is part of $S$ its probability cannot rise above 1, so every probability sits between 0 and 1. Strict positivity fails for the impossible event, whose probability is 0. Values below 0 or above 1 are forbidden outright, so the last two choices are wrong.
Q5
medium
A box holds 2 white balls and 3 black balls, identical apart from colour. One ball is drawn at random and only its colour is recorded. Consider these statements.
(i) The sample space of the experiment is $\{\text{white},\ \text{black}\}$.
(ii) The sample space has 5 sample points, one for each ball in the box.
Which statement is correct?
ABoth (i) and (ii)
BOnly (i)
COnly (ii)
DNeither (i) nor (ii)
Show answer and explanation
Correct answer: B - Only (i)
The experiment records only the colour, so the possible results are 'white' and 'black' and the sample space holds just those two sample points. Statement (ii) counts the balls rather than the recorded results, and five balls still show only two colours. So (i) alone is correct, and the choices that accept (ii) or reject (i) are wrong.
Q6
medium
Assertion (A): A bag holds only red and yellow balls, and the probability of drawing a red ball is $\frac{3}{8}$, so the probability of drawing a yellow ball is $\frac{5}{8}$. Reason (R): For every event $E$, $P(E) + P(\text{not } E) = 2$.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: C - A is true, but R is false
With only two colours in the bag, drawing a yellow ball is the complement of drawing a red one, so its probability is $1-\frac{3}{8}=\frac{5}{8}$ and the assertion is true. The reason states the wrong total: an event and its complement have probabilities adding up to $1$, not $2$. So A is true while R is false.
Practice the full Probability bank free
All 150 questions with timed practice, instant scoring, and explanations. Free forever.