You are playing a game that involves drawing three numbers from a hat. There are 25 pieces of paper numbered 1 to 25 in the hat. Each number is replaced after it is drawin. What is the probability that each number is greater than 20 or less than 4 ?
To determine the probability of each number being greater than 20 or less than 4 when three numbers are drawn, we need to first count the total number of possible outcomes and then count the number of favorable outcomes.
1. Total number of possible outcomes:
Since there are 25 pieces of paper numbered 1 to 25, and each number is replaced after being drawn, the total number of possible outcomes for each draw is 25.
Since there are three draws, the total number of possible outcomes will be calculated by multiplying the number of outcomes for each draw:
Total possible outcomes = 25 * 25 * 25 = 15,625
2. Number of favorable outcomes:
Since we want each number to be greater than 20 or less than 4, we can calculate the number of favorable outcomes.
Numbers greater than 20: There are 4 numbers greater than 20, namely 21, 22, 23, and 24. For each of the three draws, the number of possible outcomes will be 4.
Numbers less than 4: There are 3 numbers less than 4, namely 1, 2, and 3. For each of the three draws, the number of possible outcomes will be 3.
Since we want each number to fall within both conditions, we can calculate the favorable outcomes by multiplying the favorable outcomes for each condition:
Favorable outcomes = (4 * 4 * 4) * (3 * 3 * 3) = 64 * 27 = 1,728
3. Probability calculation:
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total possible outcomes
Probability = 1,728 / 15,625 ≈ 0.11 or 11%
Therefore, the probability that each number drawn is greater than 20 or less than 4 is approximately 11%.