Introduction:

Dilution plating is a widely used technique in microbiology for isolating bacterial colonies from a mixed culture. When multiple bacterial populations are present in equal proportions, understanding the probability of obtaining a specific type of colony becomes important, especially when only a few colonies are formed after plating. This article addresses a common scenario where two bacterial populations, X and Y, are mixed in equal proportions, and the probability of obtaining one colony from each population is explored.

The Scenario:

In this case, a bacterial culture contains two populations, X and Y, in equal proportions. The culture is then diluted and plated onto an agar medium. Due to the extent of dilution, only two colonies are observed to grow. The question is: What is the probability that one colony will be from population X and the other from population Y?

Understanding the Problem:

The key to solving this problem lies in recognizing that, with equal proportions of X and Y in the culture, each colony that grows on the plate has an equal chance of being derived from either population X or population Y. This is a typical case of a random process with two possible outcomes.

Step-by-Step Calculation:

1. Total number of colonies: Since two colonies were obtained, there are two possible events:

   • Colony 1 can be from population X, and Colony 2 can be from population Y.

   • Colony 1 can be from population Y, and Colony 2 can be from population X.

2. Probability of each event: Since the bacteria are in equal proportions, the probability of either colony being from population X or Y is 50% or 0.5.

3. Possible combinations: There are four possible combinations of colony types for the two colonies:

   • Both colonies are from X.

   • Both colonies are from Y.

   • One colony is from X and the other from Y.

   • One colony is from Y and the other from X.

4. Counting favorable outcomes: Out of the four possibilities, two outcomes correspond to having one colony from each population (X and Y). These are:

   • Colony 1 is from X and Colony 2 is from Y.

   • Colony 1 is from Y and Colony 2 is from X.

5. Calculating the probability: Since two out of the four possibilities are favorable, the probability of obtaining one colony from X and the other from Y is:

   P(one from X, one from Y)=2/4= 50%

Conclusion:

The probability that one colony will be from X and the other from Y in this dilution plating scenario is 50%. This result is based on the assumption of equal proportions of each population in the culture and the random nature of colony formation.

Answer:

C. 50%