It is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an even number or a number less than 8.
To find the probability that the pointer will stop on an even number or a number less than 8, we need to determine how many favorable outcomes there are out of the total possible outcomes.
The favorable outcomes would be landing on an even number or landing on a number less than 8.
There are four even numbers (2, 4, 6, and 8) and seven numbers less than 8 (1, 2, 3, 4, 5, 6, and 7). However, there is an overlap between these two sets, as numbers 2, 4, 6 are both even and less than 8. Therefore, we need to subtract the overlap to avoid double counting.
So, there are 4 even numbers, 7 numbers less than 8, and an overlap of 3 numbers.
Total favorable outcomes = 4 + 7 - 3 = 8
The spinner has 8 regions in total.
Total possible outcomes = 8
Therefore, the probability that the pointer will stop on an even number or a number less than 8 is given by:
Probability = (Total favorable outcomes) / (Total possible outcomes) = 8/8 = 1
So, the probability is 1 or 100%.