# DBT JRF 2022 — Question 28

Exam: DBT JRF 2022 · Section: A · Topic: Microbiology › Dilution Plating & Probability · Difficulty: Medium

## Question

A culture contains two bacterial populations 'X' and 'Y' in equal proportion. On dilution plating only two colonies were obtained due to excessive dilution. The probability that one will be X and other will be Y is:

## Options

- **A.** 100%
- **B.** 75%
- **C.** 50%
- **D.** 25%

## Answer

Option C

## Explanation

Dilution plating and probability of obtaining one X and one Y colony: The culture contains equal proportions X and Y, so $P(X) = P(Y) = \frac{1}{2}$ . With only 2 colonies obtained, the probability of getting exactly 1 X and 1 Y: This is a binomial probability with $n = 2$ , $k = 1$ (one success out of two trials): $P(1X, 1Y) = \binom{2}{1} \times \left(\frac{1}{2}\right)^1 \times \left(\frac{1}{2}\right)^1 = 2 \times \frac{1}{4} = \frac{1}{2} = 50\%$ The factor of 2 accounts for the two arrangements: XY or YX. Answer: 50% (Option 3).

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