Start learning →

AP Intermediate 2nd Year Probability — practice questions

Explore 51 free Probability questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Probability with Quill →

Probability questions and exercises with answers

Showing questions 1–30 of 51.

Find $\displaystyle\int x^4\,dx$.Read the answer and worked solution →Find $\displaystyle\int \sin x\,dx$.Read the answer and worked solution →Evaluate $\displaystyle\int_{0}^{\pi/2} \sin x\,dx$.Read the answer and worked solution →Find $\displaystyle\int 2x \cos(x^2)\,dx$.Read the answer and worked solution →Find $\displaystyle\int x e^x\,dx$.Read the answer and worked solution →Find $\displaystyle\int \dfrac{1}{(x-1)(x+1)}\,dx$.Read the answer and worked solution →P(drawing an Ace OR King from a deck) =Read the answer and worked solution →Two dice rolled. P(sum = 7) =Read the answer and worked solution →Bayes' theorem relates P(A|B) and P(B|A):Read the answer and worked solution →Number of ways to arrange 5 distinct books on a shelf:Read the answer and worked solution →Number of ways to choose 3 students from a class of 10:Read the answer and worked solution →A box has 5 red, 3 blue marbles. Probability of drawing 2 red and 1 blue in any order (without replacement, 3 draws):Read the answer and worked solution →For a Poisson distribution with mean λ = 3, P(X = 2):Read the answer and worked solution →Standard deviation has the same units as:Read the answer and worked solution →For 50 students with mean score 60 and variance 25, the coefficient of variation (sigma/mean × 100%):Read the answer and worked solution →P(picking a king OR a heart from 52 cards):Read the answer and worked solution →Two events A and B: P(A) = 0.3, P(B) = 0.4, P(A and B) = 0.1. Are they independent?Read the answer and worked solution →5 cards drawn from a standard deck. Probability all 5 are aces:Read the answer and worked solution →Number of distinguishable arrangements of letters in 'STATISTICS':Read the answer and worked solution →Conditional probability P(A | B) is defined as:Read the answer and worked solution →In a survey, 60% read newspaper A, 40% read B, 20% read both. P(reading neither):Read the answer and worked solution →Binomial distribution: P(X = k) for n trials, success probability p:Read the answer and worked solution →E(X) and Var(X) for fair coin tossed n times (success = heads, p = 0.5):Read the answer and worked solution →Two cards drawn from a deck (no replacement). P(both kings):Read the answer and worked solution →The probability that a marksman will hit a target is given as $\frac{1}{5}$. Then the probability that at least once hit in 10 shots isRead the answer and worked solution →The number of elements in the sample space when a coin is tossed twice is:Read the answer and worked solution →The probability of a sure event is:Read the answer and worked solution →The probability of an impossible event is:Read the answer and worked solution →For any event A, $P(\text{not }A)$ equals:Read the answer and worked solution →If A and B are mutually exclusive events, then $P(A\cap B)$ equals:Read the answer and worked solution →

Worked practice questions

Find $\displaystyle\int x^4\,dx$.

  1. $5x^5 + C$
  2. $\dfrac{x^5}{5} + C$
  3. $x^5 + C$
  4. $4x^3 + C$
Show answer and solution

Correct answer: B. $\dfrac{x^5}{5} + C$

Power rule for integration: $\displaystyle\int x^n\,dx = \dfrac{x^{n+1}}{n+1} + C$ for $n \neq -1$. Plug $n = 4$: $\dfrac{x^5}{5} + C$. Option A is the *derivative* of $x^4$, not the integral. Always check by differentiating your answer.

Open this question →

Find $\displaystyle\int \sin x\,dx$.

  1. $\cos x + C$
  2. $-\cos x + C$
  3. $-\sin x + C$
  4. $\sin x + C$
Show answer and solution

Correct answer: B. $-\cos x + C$

$\dfrac{d}{dx}(-\cos x) = \sin x$, so $\displaystyle\int \sin x\,dx = -\cos x + C$. Mnemonic: differentiating gives a negative on the sine term ($\dfrac{d}{dx} \cos x = -\sin x$). To reverse, you keep the sign that makes the derivative *positive* $\sin x$, which is the $-\cos x$ choice.

Open this question →

Evaluate $\displaystyle\int_{0}^{\pi/2} \sin x\,dx$.

  1. $-1$
  2. $1$
  3. $\pi/2$
  4. $0$
Show answer and solution

Correct answer: B. $1$

$\displaystyle\int_{0}^{\pi/2} \sin x\,dx = [-\cos x]_{0}^{\pi/2} = -\cos(\pi/2) + \cos(0) = -0 + 1 = 1$. Geometric interpretation: this is the area under one quarter of the sine curve from $0$ to $\pi/2$, which equals exactly $1$ in standard units.

Open this question →

How to practise

  1. Choose a Probability question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Probability practice for AP Intermediate 2nd Year. Read explanations as you go. No signup form needed to start.

Practise Probability →

More Mathematics topics

Vector Algebra and 3D GeometryContinuity, Differentiability & DerivativesIntegrals and ApplicationsLinear ProgrammingRelations, Functions & Inverse TrigonometryDifferential EquationsDeterminantsMatrices and Determinants