Question - Probability of Landing on a Factor of 16 and Even Number
Solution:
To solve this problem, let's look at the two events:1. Landing on a factor of 162. Landing on an even numberConsidering the first event, the factors of 16 are 1, 2, 4, 8, and 16. From the spinner, we want to find the numbers that are factors of 16. The spinner contains the numbers 1, 2, 4, 6, 7, 8, and 9. The factors of 16 present on the spinner are 1, 2, 4, and 8. There are 4 favorable outcomes out of 7 possible outcomes, so the probability of the first event is 4/7.For the second event, we need to find the probability of landing on an even number. The even numbers on the spinner are 2, 4, 6, and 8. There are 4 even numbers out of 7 possible outcomes, so the probability of the second event is also 4/7.Now, these two events are independent because the result of the first spin does not affect the result of the second spin. Therefore, the combined probability of both events occurring is the product of their individual probabilities:Probability of landing on a factor of 16 and then an even number = (Probability of landing on a factor of 16) * (Probability of landing on an even number)= (4/7) * (4/7)= 16/49Therefore, the probability of landing on a factor of 16 and then landing on an even number when spinning the spinner twice is 16/49.
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