Problem:
An urn contains 6 white and 4 black balls. A dice is rolled and the number of balls equal to the number obtained on the dice are drawn from the urn. Find the probability that the balls drawn are all black.

Solution:

Step 1: Determine the total number of possible outcomes.
Since a dice is rolled, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).

Step 2: Calculate the probability of drawing all black balls for each outcome.
To calculate the probability of drawing all black balls for each outcome, we need to consider the number of black balls and the total number of balls drawn.

For each outcome, the number of balls drawn from the urn is equal to the number obtained on the dice. Therefore, we need to consider the following cases:

- If the outcome is 1, we draw 1 ball from the urn.
- If the outcome is 2, we draw 2 balls from the urn.
- If the outcome is 3, we draw 3 balls from the urn.
- If the outcome is 4, we draw 4 balls from the urn.
- If the outcome is 5, we draw 5 balls from the urn.
- If the outcome is 6, we draw 6 balls from the urn.

Case 1: Outcome is 1
Number of black balls drawn = 0
Number of possible outcomes = 1

Case 2: Outcome is 2
Number of black balls drawn = 0
Number of possible outcomes = 1

Case 3: Outcome is 3
Number of black balls drawn = 0
Number of possible outcomes = 1

Case 4: Outcome is 4
Number of black balls drawn = 0
Number of possible outcomes = 1

Case 5: Outcome is 5
Number of black balls drawn = 0
Number of possible outcomes = 1

Case 6: Outcome is 6
Number of black balls drawn = 0
Number of possible outcomes = 1

Step 3: Calculate the probability of each case.
The probability of each case can be calculated by dividing the number of favorable outcomes (number of black balls drawn) by the total number of possible outcomes.

Case 1: Outcome is 1
Probability = Number of black balls drawn / Number of possible outcomes = 0/1 = 0

Case 2: Outcome is 2
Probability = Number of black balls drawn / Number of possible outcomes = 0/1 = 0

Case 3: Outcome is 3
Probability = Number of black balls drawn / Number of possible outcomes = 0/1 = 0

Case 4: Outcome is 4
Probability = Number of black balls drawn / Number of possible outcomes = 0/1 = 0

Case 5: Outcome is 5
Probability = Number of black balls drawn / Number of possible outcomes = 0/1 = 0

Case 6: Outcome is 6
Probability = Number of