Problem:
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is:

Solution:

To find the probability that all the balls are white, we need to calculate the probability of drawing two white balls in a row.

Step 1: Determine the total number of possible outcomes

In the urn, there are 5 balls. When we draw two balls, there are a total of 5C2 = 10 possible outcomes. Here, 5C2 represents the number of combinations of 5 objects taken 2 at a time.

Step 2: Determine the number of favorable outcomes

Since two balls are drawn and found to be white, we know that the first ball drawn is white and the second ball drawn is also white. We can calculate the number of favorable outcomes by considering the possible white balls that can be drawn.

There are 5 white balls in the urn. When we draw the first ball, there are 5 possible white balls. After drawing the first white ball, there are 4 white balls left in the urn. Therefore, when we draw the second ball, there are 4 possible white balls.

The number of favorable outcomes is the product of the number of possible white balls for each draw: 5 * 4 = 20.

Step 3: Calculate the probability

The probability of an event is defined as the number of favorable outcomes divided by the total number of possible outcomes.

In this case, the probability of drawing two white balls is 20/10 = 2.

However, we need to find the probability that all the balls in the urn are white. Since we know that the first two balls drawn are white, the remaining three balls in the urn must also be white for all the balls to be white.

Therefore, the probability that all the balls are white is the same as the probability of drawing two white balls, which is 2/10 = 1/5 = 0.5.

Answer:
The probability that all the balls in the urn are white is 1/2.