Statistics and Probability

Lakshya NDA

Learn data interpretation, central tendency and probability logic for objective questions.

Level

Exam-focused

Study Time

22 min

Exam Relevance

High (scoring section when basics are clear)

Statistics block

Frequency distribution and graphical interpretation.
Mean, median, mode comparisons.
Variance and standard deviation basics.
Correlation and regression idea level understanding.

Probability block

Sample space and event logic.
Mutually exclusive and exhaustive events.
Conditional probability and Bayes theorem.
Binomial distribution base idea.

Exam strategy

Define event symbols first.
Draw quick table/tree where possible.
Reduce fraction only at final step to avoid arithmetic slips.

Common mistakes

Confusing P(A|B) with P(B|A).
Wrong denominator in conditional probability.
Using average formula blindly without checking frequency weights.

Chapter-end mini quiz

5 quick questions from the question bank.

Question 1

If a coin is tossed till the first head appears, then what will be the sample space?

$\{H\}$$\{TH\}$$\{T, HT, HHT, HHHT, \ldots\}$$\{H, TH, TTH, TTTH, \ldots\}$

Question 2

A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is $\dfrac{1}{7}$ and that of the wife's selection is $\dfrac{1}{5}$. If the events are independent, then the probability of which one of the following is $\dfrac{11}{35}$?

At least one of them will be selectedOnly one of them will be selectedNone of them will be selectedBoth of them will be selected

Question 3

What is the value of $k$?

$1/2$$1/3$$1/4$$1/5$

Question 4

If $A$ and $B$ are two events such that $2P(A) = 3P(B)$, where $0 < P(A) < P(B) < 1$, then which one of the following is correct?

$P(A|B) < P(B|A) < P(A \cap B)$$P(A \cap B) < P(B|A) < P(A|B)$$P(B|A) < P(A|B) < P(A \cap B)$$P(A \cap B) < P(A|B) < P(B|A)$

Question 5

A special dice with numbers $1, -1, 2, -2, 0$ and $3$ is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero?

$\dfrac{1}{72}$$\dfrac{1}{8}$$\dfrac{7}{72}$$\dfrac{25}{216}$

Source Base

NCERT statistics and probability basics
CBSE data handling and conditional probability exercises

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