Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.

Question

Jody checked the temperature 12 times on Monday, and the last digit of the temperature was odd six times more than it was even. On Tuesday, she checked it 18 times and the last digit was odd eight times more than it was even. Determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks.

A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.

B. The Monday series is closer because 6/12 is closer to 0.5 than is 8/18.

C. The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.

D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.

Answer 1

To determine which series is closer to the 50/50 ratio of odd/even, we need to compare the ratios of odd to even numbers in each series.

Let's start with the Monday series:
- Jody checked the temperature 12 times, and the last digit was odd six times more than it was even.
- This means that there were 6 odd numbers and 6 + 6 = 12 even numbers.
- The ratio of odd to even numbers is 6/12, which simplifies to 1/2.

Now let's move to the Tuesday series:
- Jody checked the temperature 18 times, and the last digit was odd eight times more than it was even.
- This means that there were 10 odd numbers (8 more than the even numbers) and 18 - 10 = 8 even numbers.
- The ratio of odd to even numbers is 10/18, which does not simplify further.

Comparing the ratios:
- Option A states that the Monday series is closer because 1/6 is closer to 1/2 than 1/8. However, this is incorrect because the ratio for the Monday series is 1/2, not 1/6.
- Option B states that the Monday series is closer because 6/12 is closer to 0.5 than 8/18. This is correct because 6/12 simplifies to 1/2, which is closer to 0.5 than 8/18.
- Option C states that the Tuesday series is closer because 13/18 is closer to 0.5 than 9/12. However, 13/18 is actually further from 0.5 than 9/12.
- Option D suggests that the series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series. However, we have already determined the ratios for both series, so this option is not correct.

Therefore, the correct answer is B. The Monday series is closer because 6/12 is closer to 0.5 than 8/18.