For a probability of a random variable X is given belowX | 1 | 2 | 4 | 5 | 6Y | 0.15 | 0.25 | 0.2 | 0.3 | 0.1What is The Standard deviation of X ?

Option d: 1.72. Solution: Probability of Drawing One Spade and One Heart Total cards in a standard deck = 52 - Spade cards = 13 - Heart cards = 13 Two cards are drawn together. We want the probability of getting 1 spade and 1 heart. Step 1: Calculate total ways to choose 2 cards Total ways = (52 choose 2) = 52 × 51/2 = 1326 Step 2: Calculate favorable ways To get exactly 1 spade and 1 heart: Favorable ways = (13 choose 1) × (13 choose 1) = 13 × 13 = 169 Step 3: Probability calculation P = 169/1326 Dividing the numerator and the denominator by 13: P = 13/102 Hence, Option D is the correct answer.

ProbabilityMCQMTP Mar 22Question 3405 of 187

All Questions

For a probability of a random variable $\displaystyle X$ is given belowX | 1 | 2 | 4 | 5 | 6Y | 0.15 | 0.25 | 0.2 | 0.3 | 0.1What is The Standard deviation of $\displaystyle X$ ?

Options

\displaystyle 1.49

\displaystyle 1.56

\displaystyle 1.69

\displaystyle 1.72

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Correct Answer

✅ Option d — $\displaystyle 1.72$

All Options:

A $\displaystyle 1.49$
B $\displaystyle 1.56$
C $\displaystyle 1.69$
D $\displaystyle 1.72$

Detailed Solution & Explanation

**Probability of Drawing One Spade and One Heart** Total cards in a standard deck = 52 - Spade cards = 13 - Heart cards = 13 Two cards are drawn together. We want the probability of getting 1 spade and 1 heart. **Step 1: Calculate total ways to choose 2 cards**

\text{Total ways} = \binom{52}{2} = \frac{52 \times 51}{2} = 1326

**Step 2: Calculate favorable ways** To get exactly 1 spade and 1 heart:

\text{Favorable ways} = \binom{13}{1} \times \binom{13}{1} = 13 \times 13 = 169

**Step 3: Probability calculation**

P = \frac{169}{1326}

Dividing the numerator and the denominator by 13:

P = \frac{13}{102}

Hence, **Option D** 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

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.

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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For a probability of a random variable X\displaystyle XX is given belowX | 1 | 2 | 4 | 5 | 6Y | 0.15 | 0.25 | 0.2 | 0.3 | 0.1What is The Standard deviation of X\displaystyle XX?