Question

mariah has a spinner that has 10 equal sections, each containing a different number from 1 to 10. mariah determines about how many times the spinner will land on a number that is greater than 7 in 250 spins, and her work is shown below. p(number greater than 7) = \frac{numbers greater than 7}{total number of sections} \cdot number of spins = \frac{4}{10}(250) = 100 what mistake did mariah make, if any? mariah has the formula reversed; it should be the total number of sections over the numbers greater than 7. mariah should have used a 3 in the numerator because there are 3 numbers greater than 7. mariah should multiply by the number of sections in the spinner rather than the total number of spins. mariah calculated the prediction correctly and did not make any mistakes.

Explanation:

Step1: Identify numbers greater than 7

Numbers from 1 - 10 greater than 7 are 8, 9, 10. So there are 3 such numbers.

Step2: Analyze Mariah's work

Mariah used 4 in the numerator of the probability - fraction instead of 3 when calculating \(P(\text{number greater than }7)\). The correct formula for the expected number of times the spinner lands on a number greater than 7 is \(P(\text{number greater than }7)=\frac{\text{Numbers greater than }7}{\text{Total number of sections}}\cdot\text{Number of spins}=\frac{3}{10}(250)\).

Answer:

Mariah should have used a 3 in the numerator because there are 3 numbers greater than 7.