a spinner is spun whose central angles are all 45 degrees. #'s 1-8 on wheel. What is the probability that it lands on 5 if you know the following?

a. it lands on an odd #
b. it lands on a # greater than 3
c. it does not land on 7 or 8
d. it lands on a factor of 10

If it is a random spin, the probability is always 1/8.

To find the probability of landing on a specific number on the spinner, we need to determine the total number of equally likely outcomes and the number of favorable outcomes. Let's break down each scenario and calculate the probability accordingly:

a. The spinner lands on an odd number: There are four odd numbers on the spinner, which are 1, 3, 5, and 7. Since the central angle for each number is 45 degrees, the probability of landing on an odd number is 4/8 or 1/2.

b. The spinner lands on a number greater than 3: There are five numbers greater than 3 on the spinner, which are 4, 5, 6, 7, and 8. Therefore, the probability of landing on a number greater than 3 is 5/8.

c. The spinner does not land on 7 or 8: There are six numbers on the spinner excluding 7 and 8. Thus, the probability of not landing on 7 or 8 is 6/8 or 3/4.

d. The spinner lands on a factor of 10: The factors of 10 are 1, 2, 5, and 10. However, there is no number on the spinner that represents 10. Hence, the probability of landing on a factor of 10 is 3/8.

Therefore, the probability of the spinner landing on number 5, given the above conditions, would be:

a. 1/2
b. 5/8
c. 3/4
d. 3/8

Please note that these probabilities are independent of each other since each condition represents a distinct event.