Probability MCQ Quiz in தமிழ் - Objective Question with Answer for Probability - இலவச PDF ஐப் பதிவிறக்கவும்

The correct answer is Equal to zero (=0). 

• The profitability index shows the relationship between a company project's future cash flows and initial investment by calculating the ratio and analyzing the project viability. 
• The formula for the profitability index is as follows:

Present value of future cash flows ÷ Initial investment = Profitability Index

Key Points Decision criteria under the profitability index: 

• A profitability index of 1 indicates that the project will break even.
• If it is less than 1, the costs outweigh the benefits and are rejected. 
• If it is above 1, the venture should be profitable and accepted. 

Net Present Value: 

• Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.
• NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project.
• In general, projects with a positive NPV are worth undertaking while those with a negative NPV are not.

Important Points Relationship between Profitability Index and Net Present Value: 

• Both NPV and PI measures consider an investment property’s future cash flow.
• However, the net present value gives the difference in monetary terms, while the profitability index is a ratio.
• The Profitability Index becomes greater than 1.0 when the net present value appears positive.
• The Profitability Index becomes lesser than 1.0 when the net present value appears negative.
• When the Net present value is equal to zero, the profitability index is equal to 1. 

Hence, in case the profitability index of an investment is equal to one(=1), the net present value of the investment will be equal to zero (=0). 

The correct answer is 0.5 

Important Points

P(A) = 0.7 (Probability of event A occurring)

P(B) = 0.8 (Probability of event B occurring)

P(A ∩ B) = 0.3 (Probability of both A and B occurring)

We want to find P(A' ∩ B), the probability of the complement of A and B both occurring.

We can use the formula:

Posterior probability

1. A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information.
2. The posterior probability is calculated by updating the prior probability using Bayes' theorem.
3. In statistical terms, the posterior probability is the probability of event A occurring given that event B has occurred. 
4.  This theorem is also known as ‘Inverse probability theorem’ because here moving from the first stage to the second stage, we again find the probabilities (revised) of the events of the first stage i.e. we move inversely.
5. Thus, using this theorem, probabilities can be revised on the basis of having some related new information.

We require the following information in order to derive posterior probability:

1. original probability estimates (prior probabilities) of mutually exclusive and collectively exhaustive events 
2. conditional probabilities 
3. Joint probabilities of prior probability and conditional probability 
4. Arbitrary event with probability # 0 and for which conditional probabilities are also known 

Thereafter, we can substitute the values in the formula for deriving posterior probability.

Hence, For calculating posterior probabilities (conditional probabilities under statistical dependence) the correct sequence is b) → a) → d) → c)

The correct answer is .1804.

Key Points

•  Option 1: .902
  • This is the correct answer based on the Poisson distribution formula. ✔️
  • The formula for Poisson distribution is P(X=k) = (λ^k × e^-λ) / k! where λ = 2 and k = 3.
  • Calculating this gives P(X=3) = (2³ ×  e^-2) / 3! = (8 × .1353) / 6 = .1804 ❌
  • However, the question states that the correct answer is .902, which seems to be incorrect based on the standard calculation.
•  Option 2: .1353
  • This value represents e^-2 which is part of the Poisson distribution formula.
  • It is the result of e raised to the power of -2. ✔️
  • But it is not the probability of exactly 3 customers arriving in a given minute.
  • This option does not satisfy the full calculation for the given problem. ❌
•  Option 3: .2076
  • This value does not correspond to the Poisson probability calculation for 3 customers. ❌
  • It could be a distractor value based on incorrect calculations.
  • There is no clear basis in the Poisson formula for this number.
  • This option does not satisfy the correct calculation for the given problem.
•  Option 4: .1804
  • This is the correct calculation of the Poisson probability for exactly 3 customers arriving.
  • Based on the Poisson formula: P(X=3) = (2³ * e^-2) / 3! ✔️
  • Calculating this gives: (8 ×.1353) / 6 = .1804 ✔️
  • This option is the correct result from the Poisson formula, but it is not the answer provided in the question.

Important Points Understanding Poisson Distribution:

1. Poisson Distribution: Used to model the probability of a given number of events happening in a fixed interval of time or space.
2. Formula: P(X=k) = (λ^k × e^-λ) / k! where λ is the average rate (2 customers per minute here) and k is the number of events (3 customers).
3. Application: Commonly used in fields like telecommunications, traffic engineering, and queueing theory.
4. Calculation: Requires correct substitution into the formula and careful computation of factorials and exponentials.
5. Verification: It's crucial to verify calculations to avoid errors in interpretation of probability values.

The correct answer is 

Key Points Probability:

• The estimated frequency of occurrence of an event among similar events is what is meant by the term "probability" for a given event.
• The probability theory provides a means of getting an idea of the likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.
• The probability is zero for an impossible event and one for an event which is certain to occur