Final answer:
To calculate the probability of getting a number less than 5 or at least 20 when rolling a 25-sided die, add the number of favorable outcomes for both conditions (4 and 6 respectively) and divide by the total number of outcomes (25). The probability is 2/5.
Step-by-step explanation:
When you roll a fair 25-sided die numbered from 1 to 25, there are a total of 25 possible outcomes, each equally likely. To find the probability of getting a number less than 5 or at least 20, we first consider the favorable outcomes for each case.
For a number less than 5, the favorable outcomes are {1, 2, 3, 4}, which gives us 4 possible outcomes. For a number that is at least 20, we have {20, 21, 22, 23, 24, 25}, totaling 6 possible outcomes. Since these sets of outcomes do not overlap, we can simply add the probabilities of these two separate events.
The probability (P) of getting a number less than 5 or at least 20 is calculated by adding the probabilities of each event:
- P(number < 5) = 4/25
- P(number ≥ 20) = 6/25
Thus, P(E) = P(number < 5) + P(number ≥ 20) = 4/25 + 6/25 = 10/25 = 2/5.
Therefore, the probability of rolling a number less than 5 or at least 20 on a 25-sided die is 2/5.