A number is drawn at random from {1,2,3,4,5,6}. What is the probability that either a number larger than 3 or an even number will occur?
To find the probability of either a number larger than 3 or an even number occurring, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes in this case are the numbers larger than 3 or the even numbers. We have three numbers larger than 3: 4, 5, and 6. We also have three even numbers: 2, 4, and 6. Notice that the number 4 is counted twice since it is both larger than 3 and an even number. Therefore, the number of favorable outcomes is 5 (3 + 2 - 1).
The total number of possible outcomes is the number of elements in the set {1, 2, 3, 4, 5, 6}, which is 6.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 5 / 6
Hence, the probability that either a number larger than 3 or an even number will occur is 5/6.