COMPETITIVE EXAM MCQs SERIES of ENVIRONMENTAL SCIENCE for UGC-NET/JRF, SLET, ARS, GATE, and other entrance tests – Statistical Approaches and Modelling in Environmental Sciences: Concepts of Probability Theory.
Syllabus Outline
- Probability in analysing uncertainty in environmental data. Applications in risk assessment, species distribution, weather prediction, and pollution modelling.
- Classical Probability (Based on known outcomes), Empirical Probability (Based on observed environmental frequencies), Bayesian Probability (utilising prior knowledge in updating probabilities), and Subjective Approaches.
- Rules of probability: addition and multiplication rules.
- Conditional probability and independent events.
- Introduction to discrete and continuous probability distributions.
- Application of probability in modelling rainfall occurrence, pollutant levels, and species encounters.
This quiz contains concept-based, the most frequently asked 25 MCQs of “Statistical Approaches and Modelling in Environmental Sciences: Concepts of Probability Theory”. Each question has a single correct/most appropriate answer.
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1. If two environmental events are mutually exclusive, their joint probability is:
A) 1
B) 0
C) Sum of individual probabilities
D) Product of individual probabilities
2. If P(A) = 0.6 and P(B) = 0.4, and events A and B are independent, then P(A ∩ B) equals:
A) 0.24
B) 1.0
C) 0.2
D) 0.4
3. In environmental risk assessment, Type I error represents:
A) Accepting a false hypothesis
B) Rejecting a true hypothesis
C) Correct decision making
D) Insufficient data collection
4. If the coefficient of variation for rainfall data is 25%, and the mean is 100mm, the standard deviation is:
A) 4mm
B) 25mm
C) 75mm
D) 125mm
5. In the Poisson distribution, the variance is:
A) Always greater than the mean
B) Always less than the mean
C) Equal to the mean
D) Independent of the mean
6. In a watershed management study, the probability of extreme rainfall in any given year is 0.15. Using geometric distribution, what is the probability that the first extreme rainfall occurs in the 3rd year?
A) 0.108375
B) 0.15
C) 0.45
D) 0.7225
7. An environmental scientist uses stratified sampling to study biodiversity. If stratum A has 200 trees with variance 16, and stratum B has 300 trees with variance 25, the optimal allocation ratio (nA:nB) is:
A) 2:3
B) 8:15
C) 4:5
D) 1:1
8. Uncertainty in environmental data analysis primarily arises due to:
I – Measurement errors
II – Natural variability
III – Model limitations
A) I only
B) I and II
C) II only
D) I, II and III
9. In species distribution modelling, probability does not help address uncertainty by:
I – Providing exact locations where species will be found
II – Quantifying the likelihood of species presence across different habitats
III – Eliminating the need for field surveys
IV – Predicting exact population numbers
A) I Only
B) II Only
C) I, III and IV
D) I, II, III and IV
10. In pollution modelling, probabilistic approaches are essential for accounting for variability in:
I – Emissions
II – Dispersion
III – Environmental Conditions
IV – Predicted pollution
A) I and II
B) I, II, and III
C) IV only
D) I, II, III and IV
11. In integrated environmental assessment models, uncertainty propagation through multiple linked sub-models is best handled by:
A) Using average values for all parameters and ignoring uncertainty in sub-models
B) Applying error propagation formulas, assuming independence with average values for all parameters
C) Probabilistic simulation considering parameter correlations and model structure uncertainty
D) Applying error propagation formulas to avoid uncertainty in sub-models
12. When combining multiple environmental data sources with different uncertainty characteristics, the optimal approach is:
A) Using the most accurate source only
B) Simple averaging of all sources
C) Weighted combination based on inverse variance weighting and correlation structure
D) Random selection from available sources
13. Bayesian probability is particularly valuable in environmental science because it:
I – It relies on current data
II – Combines prior knowledge with new observational evidence
III – It provides deterministic outcomes
IV – It uses computational-based artificial intelligence
A) I only
B) II only
C) II and III
D) I, III and IV
14. In Bayesian updating for contamination assessment, if prior P(Contamination) = 0.3 and the likelihood of a positive test given contamination is 0.9 with a false positive rate of 0.1, what is the posterior probability after a positive test?
A) 0.794
B) 0.3
C) 0.9
D) 0.27
15. Subjective probability elicitation from three experts yields contamination risk estimates of 0.2, 0.35, and 0.4. Using equal weighting, the combined subjective probability is:
A) 0.317
B) 0.4
C) 0.2
D) 0.35
16. An ecological study applies empirical probability using 5 years of data showing species migration in 15 out of 20 observed seasons. The empirical probability of migration is:
A) 0.25
B) 0.75
C) 0.5
D) 0.8
17. For any environmental event A, P(A) + P(A’) equals:
A) 0
B) 0.5
C) 1
D) P(A) × 2
18. In habitat assessment, P(Suitable Vegetation) = 0.7 and P(Adequate Water) = 0.5. If these factors are independent, P(Suitable Vegetation ∩ Adequate Water) is:
A) 1.2
B) 0.35
C) 0.85
D) 0.2
19. Two environmental events A and B are independent if:
A) P(A|B) = P(A)
B) P(A ∩ B) = 0
C) P(A ∪ B) = 1
D) P(A) = P(B)
20. Marine biodiversity survey finds P(Rare Species|Deep Water) = 0.4, P(Deep Water) = 0.6. If P(Rare Species) = 0.3, are “Rare Species” and “Deep Water” independent?
A) Yes, because P(Rare Species|Deep Water) ≠ P(Rare Species)
B) No, because P(Rare Species|Deep Water) ≠ P(Rare Species)
C) Yes, because P(Rare Species|Deep Water) ≠ P(Deep Water)
D) Cannot determine from the given information
21. Groundwater contamination analysis shows P(Contamination|Industrial Zone) = 0.6, P(Industrial Zone) = 0.3, P(Contamination|Residential Zone) = 0.1, P(Residential Zone) = 0.4, P(Contamination|Agricultural Zone) = 0.2, P(Agricultural Zone) = 0.3. What is the total probability of contamination?
A) 0.28
B) 0.9
C) 0.24
D) 0.18
22. A discrete probability distribution is most appropriate for modelling:
A) Continuous pollutant concentrations
B) Number of species in a habitat
C) Temperature measurements
D) Wind speed variations
23. A continuous probability distribution is best suited for modelling:
A) Number of pollution incidents
B) Count of endangered species
C) Rainfall amounts
D) Number of sampling sites
24. Pollutant levels follow a normal distribution with a mean of 50 μg/m³ and a standard deviation of 10 μg/m³. What is the probability that a randomly selected measurement exceeds 60 μg/m³?
A) 0.159
B) 0.841
C) 0.5
D) 0.341
25. A flood risk assessment uses classical probability for a fair die representing six equally likely precipitation scenarios. The extreme precipitation probability (scenarios 5 or 6) is:
A) 1/6
B) 1/3
C) 1/2
D) 2/3
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References
- Gupta, S.P. (2020) Statistical Methods, Sultan Chand & Sons, 44th edition.
- Manly, B.F.J. (2008) Statistics for Environmental Science and Management, Chapman and Hall/CRC, 2nd edition.
- Barnett, V. (2004) Environmental Statistics: Methods and Applications, Wiley, 1st edition.
