Final answer:
The probability of the spinner landing on an odd number or a number divisible by 3 is 9/14.
Step-by-step explanation:
The probability that the spinner lands on an odd number or a number that is divisible by 3 can be found by adding the probabilities of the two separate events together. Let's first calculate the probability of landing on an odd number. Out of the numbers 1 to 14, half of them are odd, so the probability is 7/14 or 1/2. Now let's calculate the probability of landing on a number divisible by 3. There are 4 numbers divisible by 3 (3, 6, 9, 12), so the probability is 4/14 or 2/7. To find the probability of either event happening, we add the probabilities together and subtract the probability of both events happening at the same time (since that's double-counted). So the probability is (1/2) + (2/7) - (1/2)(2/7) = 7/14 + 4/14 - 2/14 = 9/14.