A lottery game has balls numbered 1 through 15. If a ball is selected at random, what is the probability of selecting a ball showing an even number or the number 12?
I thought the answer would be 7 even numbers and 1 for the 12 which would be 8/15 is not an option for the answer.
Our choices are 5/4,7,4/5,7/15
Hmm 12 is already an even number! Hence you should not count 12 twice, therefore answer should be 7/15. :)
To find the probability of selecting a ball showing an even number or the number 12, we need to count the favorable outcomes and divide by the total number of possible outcomes.
There are two ways to approach this problem. Let's go through both methods:
Method 1: Counting favorable outcomes
There are a total of 15 balls, so the total number of possible outcomes is 15.
Counting the favorable outcomes:
There are 8 balls with even numbers (2, 4, 6, 8, 10, 12, 14) and 1 ball with the number 12.
So, the total number of favorable outcomes is 8 + 1 = 9.
Therefore, the probability of selecting a ball showing an even number or the number 12 is 9/15, which simplifies to 3/5.
Method 2: Using the principle of inclusion-exclusion
We can find the probability by finding the probability of selecting an even number and the probability of selecting the number 12, and then subtracting the probability of selecting both (since we counted it twice).
Probability of selecting an even number: There are 7 even numbers from 1 to 15, so the probability is 7/15.
Probability of selecting the number 12: Since there is only 1 ball with the number 12, the probability is 1/15.
Probability of selecting both an even number and the number 12: Since the number 12 is already included in the even numbers, the probability is simply the probability of selecting the number 12, which is 1/15.
Using the principle of inclusion-exclusion:
Probability of selecting an even number or the number 12 = Probability of selecting an even number + Probability of selecting the number 12 - Probability of selecting both
= 7/15 + 1/15 - 1/15
= 7/15
Therefore, the correct answer is 7/15, which matches one of the given choices.