Question

An urn contains 25 marbles which are numbered from 1 to 25 and a marble is chosen at random two times with replacement. Then the probability that both times the marble has the same number is

• A. \(\frac{1}{625}\)
• B. \(\frac{24}{25}\)
• C. \(\frac{1}{25}\)
• D. \(\frac{624}{625}\)
• E. \(\frac{2}{25}\)

Answer 1

The Correct Option is A

Given: An urn contains 25 marbles numbered from 1 to 25. A marble is chosen at random two times with replacement. We are asked to find the probability that both times the marble has the same number.

Step 1: Probability of choosing any particular marble in the first draw: 

\[ \text{Probability of choosing a particular marble} = \frac{1}{25} \]

Step 2: Since the marble is chosen with replacement, the probability of choosing the same marble again in the second draw is also:

\[ \text{Probability of choosing the same marble in the second draw} = \frac{1}{25} \]

Step 3: Total probability of both draws resulting in the same marble:

\[ \text{Total probability} = \frac{1}{25} \times \frac{1}{25} = \frac{1}{625} \]

Final Answer:

\[ \frac{1}{625} \]