Calculating Probability of Landing on Factor of 16 and Even Number
To find the probability of landing on a factor of 16 and then landing on an even number after spinning the spinner twice, let's break down the problem into two separate events:
1. Landing on a factor of 16.
2. Landing on an even number.
For the first event, we'll identify the factors of 16 from the numbers available on the spinner. The positive factors of 16 are 1, 2, 4, 8, and 16. Now, let's see which of these are present on the spinner. I can see the numbers 8 and 4 on the spinner, both of which are factors of 16.
For the second event, we'll identify which numbers are even. The even numbers on the spinner are 4, 6, and 8.
Now we calculate the probability for each event and then multiply them to find the total probability of both events happening in sequence (assuming the spinner is fair and each number has an equal chance of being landed on).
1. Probability of landing on a factor of 16:
There are two factors of 16 on the spinner (4 and 8) out of 8 possible numbers. So the probability is 2/8 or simplified to 1/4.
2. Probability of landing on an even number regardless of the first spin:
There are three even numbers on the spinner (4, 6, and 8) out of 8 possible numbers. So the probability is 3/8.
Multiplying the two probabilities together gives the final probability:
(1/4) * (3/8) = 3/32
So, the probability of landing on a factor of 16 and then landing on an even number is 3/32.
