Answer:
b, 45
Step-by-step explanation:
The spinner shown has eight congruent sections. The spinner is spun 120 times. What is a reasonable prediction for the number of times the spinner will land on an even number?
Before I begin, let's go over probability.
The probability of an event is: (the number of ways something can happen) / (total number of outcomes possible). So, for example, the probability of rolling a one on a die can be found like:
There is 1 way to roll a one, and 6 possible sides, so the probability is 1/6.
And, if we were to roll the die 60 times, we could expect about 1/6 of the times to be a one, so we should expect a one to be rolled 1/6 * 60 = 10 times.
Now, onto the problem.
Each portion is congruent (they all have the same area). Thus, there is a 1/8 chance of landing on 1, a 1/8 chance of landing on 9, etc.
5 sections are odd, while 3 sections are even. So, the chance of landing on an even number is:
(3 ways to land on an even number) / (8 possible outcomes) = 3/8
If there is a 3/8 possibility to land on even, and there are 120 outcomes, we can say that an even number statistically should be rolled 3/8 * 120 times.
3/8 * 120 = 45
Thus, the answer is b, 45 times
Just in case, let's check the answer by finding the number of times we should roll an odd number and adding it to the number of even times and if it adds up to 120, then the answer is correct.
Because there is a 5/8 chance of getting an odd number, there should be about 5/8 * 120 = 75 times that an odd number is spun.
75 + 45 = 120, so the answer is correct.
I hope this helps! Feel free to ask any questions!
</h2><h2>ANSWER</h2><h2>
</h2><h3>EXPLANATION</h3>