Skip to content

Home › Exam notes › SSC CGL › Probability & Distributions

Probability & Distributions

Paper-II Statistics (Post-specific) · Statistics Syllabus

Useful for: SSC CGL

Overview

Probability theory and standard distributions (binomial, Poisson, normal) model random outcomes.

Key points

P(A ∪ B) = P(A) + P(B) − P(A ∩ B); P(A | B) = P(A ∩ B)/P(B).
Binomial: mean np, variance npq (q = 1 − p).
Poisson: mean = variance = λ; P(X = x) = e^(−λ) λˣ/x!.
Normal: symmetric, mean = median = mode; about 68%, 95%, 99.7% within 1, 2, 3 SDs.
Standard normal z = (x − μ)/σ.

Explanation

Bayes’ theorem updates probabilities given new evidence.
Binomial variance is always less than its mean.
Poisson approximates binomial when n is large and p small (λ = np).
Area under the whole normal curve = 1.

Step by step

Identify the measure or test asked and its formula.
Organise the data (table, totals) before computing.
Interpret the result (sign, size, significance).

Examples

Binomial with n = 10, p = 0.4: mean = 4, variance = 2.4.
Poisson with λ = 2: P(X = 0) = e^(−2) ≈ 0.135.
About 95% of a normal distribution lies within ±2σ of the mean.

Traps and advanced points

Trap: Using npq as the mean.
Trap: Thinking Poisson variance differs from its mean.
Trap: Applying the 68–95–99.7 rule to skewed data.

Quick revision

Binomial np, npq.
Poisson mean = variance.
68–95–99.7.

Practice MCQs

The probability of getting a head when a fair coin is tossed once is
1. 1
2. 1/2
3. 0
4. 1/4
Read chapter notes · Similar questions
Show answer
Answer: (b) 1/2. Two equally likely outcomes.
The probability of getting a sum of 7 with two fair dice is
1. 1/36
2. 1/12
3. 7/36
4. 1/6
Read chapter notes · Similar questions
Show answer
Answer: (d) 1/6. 6 favourable outcomes out of 36.
For a binomial distribution with n = 10 and p = 0.5, the mean is
1. 0.5
2. 2.5
3. 10
4. 5
Read chapter notes · Similar questions
Show answer
Answer: (d) 5. Mean = np.
In a Poisson distribution, the mean and variance are
1. equal
2. always zero
3. mean twice the variance
4. unrelated
Read chapter notes · Similar questions
Show answer
Answer: (a) equal. Both equal λ.
About what percentage of values in a normal distribution lie within ±1 standard deviation of the mean?
1. 50%
2. 95%
3. 99.7%
4. 68%
Read chapter notes · Similar questions
Show answer
Answer: (d) 68%. 95% lie within ±2 SD.
For two mutually exclusive events A and B, P(A ∪ B) equals
1. P(A) + P(B)
2. P(A) × P(B)
3. P(A) − P(B)
4. 1
Read chapter notes · Similar questions
Show answer
Answer: (a) P(A) + P(B). They cannot occur together.

More topics in this chapter

Notes and questions are written by Kundali IQ for practice. They are not official papers; always check the latest official notification for the syllabus and pattern.