ProbabilityMCQPYQ July 21Question 3398 of 187

The value of $\displaystyle K$ for the probability density function of a variable $\displaystyle X$ is equal to: | X | P(x) ||---|---|| 0 | $\displaystyle 5k$ || 1 | $\displaystyle 3k$ || 2 | $\displaystyle 4k$ || 3 | $\displaystyle 6k$ || 4 | $\displaystyle 7k$ || 5 | $\displaystyle 9k$ || 6 | $\displaystyle 11k$ |

Options

\displaystyle \frac{1}{39}

\displaystyle \frac{1}{40}

\displaystyle \frac{1}{49}

\displaystyle \frac{1}{45}

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Correct Answer

✅ Option c — $\displaystyle \frac{1}{49}$

All Options:

A $\displaystyle \frac{1}{39}$
B $\displaystyle \frac{1}{40}$
C $\displaystyle \frac{1}{49}$
D $\displaystyle \frac{1}{45}$

Detailed Solution & Explanation

**Probability of Getting More Than 1 Head in 3 Coin Tosses** When an unbiased coin is tossed 3 times, the sample space

\displaystyle S

contains

\displaystyle 2^3 = 8

outcomes:

S = \{\text{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}\}

The event "getting more than 1 head" means getting either 2 heads or 3 heads. Let's list these outcomes: - 3 heads:

\displaystyle \{\text{HHH}\}

(1 outcome) - 2 heads:

\displaystyle \{\text{HHT, HTH, THH}\}

(3 outcomes) Total favorable outcomes =

\displaystyle 1 + 3 = 4

. Thus, the probability is:

P = \frac{4}{8} = \frac{1}{2}

Hence, **Option C** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

Key Concepts to Understand

Function

A relation from a set A (Domain) to a set B (Codomain) such that every element in A is associated with exactly one element in B. Written as f: A→B. Types include Linear, Quadratic, Polynomial, and Exponential functions.

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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