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.
The Tuesday series is closer because the 13/18 is closer to 0.5 than is 9/12.
To determine which series is closer to the 50/50 ratio of odd/even expected, we need to compare the ratios of odd to even numbers in each series.
On Monday, Jody checked the temperature 12 times. The last digit of the temperature was odd six times more than it was even. Let's calculate the ratio of odd to even numbers:
Odd numbers: 6 + 6 = 12
Even numbers: 12 - 6 = 6
Ratio of odd to even: 12/6 = 2/1 = 2
On Tuesday, Jody checked the temperature 18 times. The last digit was odd eight times more than it was even. Let's calculate the ratio:
Odd numbers: 8 + 8 = 16
Even numbers: 18 - 8 = 10
Ratio of odd to even: 16/10 = 8/5
Comparing these ratios, we can see that the ratio for Monday is 2/1 and the ratio for Tuesday is 8/5. Neither of these ratios is equal to the 50/50 ratio of odd/even expected. Therefore, the series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.
Therefore, the correct answer is D. The series closest to the theoretical 50/50 cannot be determined without knowing the number of odds and evens in each series.
To determine which series is closer to the 50/50 ratio of odd/even expected of such a series of temperature checks, we need to compare the ratios of odds to evens in each series.
Let's start by analyzing 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 + 6 = 12 odd digits and 12 - 6 = 6 even digits. So, the ratio of odds to evens in the Monday series is 12/6, which simplifies to 2/1.
Now, let's examine 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 8 + 8 = 16 odd digits and 18 - 8 = 10 even digits. So, the ratio of odds to evens in the Tuesday series is 16/10, which simplifies to 8/5.
To determine which series is closer to the 50/50 ratio of odd/even, we need to compare the ratios with the ratio of 1/1 (which represents a 50/50 ratio).
Comparing the ratios:
1. For the Monday series, the ratio is 2/1.
2. For the Tuesday series, the ratio is 8/5.
To do this, we can find the difference between each ratio and the theoretical 50/50 ratio of 1/1.
1. For the Monday series, the difference is |2/1 - 1/1| = 1/1.
2. For the Tuesday series, the difference is |8/5 - 1/1| = 3/5.
Based on the differences calculated, we can now determine the answer:
A. The Monday series is closer because 1/1 is closer to 1/2 than is 3/5.
Therefore, the correct answer is A. The Monday series is closer because 1/6 is closer to 1/2 than is 1/8.