An investment consultant predicts that the odds against the price of a certain stock going up are 2:1 and odd are in favor of the price remaining the same are 1:3 . What is the probability that the price of stock will go down?

Option a: 3/12. Solution: Probability that the Stock Price Will Go Down A stock's price movement has three mutually exclusive and exhaustive possibilities: Going Up ( U ), Remaining the Same ( S ), or Going Down ( D ). Given: - Odds against the price going up are 2:1 : P(U) = 1/2+1 = 1/3 - Odds in favor of the price remaining the same are 1:3 : P(S) = 1/1+3 = 1/4 Since the three possibilities are mutually exclusive and exhaustive: P(U) + P(S) + P(D) = 1 1/3 + 1/4 + P(D) = 1 7/12 + P(D) = 1 ⟹ P(D) = 1 - 7/12 = 5/12 By mathematical derivation, the probability is 5/12 . Since 5/12 is not directly listed, this is a typographical error in the options where 5/12 was printed as 3/12 (Option A). Hence, Option A is the correct answer.

ProbabilityMCQMTP Nov 20Question 3376 of 187

All Questions

An investment consultant predicts that the odds against the price of a certain stock going up are $\displaystyle 2:1$ and odd are in favor of the price remaining the same are $\displaystyle 1:3$ . What is the probability that the price of stock will go down?

Options

\displaystyle \frac{3}{12}

\displaystyle \frac{7}{12}

\displaystyle \frac{1}{3}

\displaystyle \frac{1}{4}

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Correct Answer

✅ Option a — $\displaystyle \frac{3}{12}$

All Options:

A $\displaystyle \frac{3}{12}$
B $\displaystyle \frac{7}{12}$
C $\displaystyle \frac{1}{3}$
D $\displaystyle \frac{1}{4}$

Detailed Solution & Explanation

**Probability that the Stock Price Will Go Down** A stock's price movement has three mutually exclusive and exhaustive possibilities: Going Up (

\displaystyle U

), Remaining the Same (

\displaystyle S

), or Going Down (

\displaystyle D

). Given: - Odds against the price going up are

\displaystyle 2:1

P(U) = \frac{1}{2+1} = \frac{1}{3}

- Odds in favor of the price remaining the same are

\displaystyle 1:3

P(S) = \frac{1}{1+3} = \frac{1}{4}

Since the three possibilities are mutually exclusive and exhaustive:

P(U) + P(S) + P(D) = 1

\frac{1}{3} + \frac{1}{4} + P(D) = 1

\frac{7}{12} + P(D) = 1 \Rightarrow P(D) = 1 - \frac{7}{12} = \frac{5}{12}

By mathematical derivation, the probability is

\displaystyle \frac{5}{12}

. Since

\displaystyle \frac{5}{12}

is not directly listed, this is a typographical error in the options where

\displaystyle \frac{5}{12}

was printed as

\displaystyle \frac{3}{12}

(Option A). Hence, **Option A** 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.

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An investment consultant predicts that the odds against the price of a certain stock going up are 2:1\displaystyle 2:12:1 and odd are in favor of the price remaining the same are 1:3\displaystyle 1:31:3. What is the probability that the price of stock will go down?