If you were to pick one day of the year at random, is it more likely that the day would be a Tuesday or that the day would fall during the month of January? Answer and explain in your own words why you chose what you chose.

It's more likely it's a Tuesday

Explanation:

The odds of it being a Tuesday is 1/7 since there's 1 day of the week that's Tuesday out of 7 total.

The odds of it being January is 1/12 because we have 1 month we want out of 12 total.

Now the question is: which fraction is larger?

For now, assume they are equal. We'll cross multiply like so

1/7 = 1/12

1*12 = 7*1

12 = 7

We get a false statement at the end, but we can fix things by replacing the equal sign with a greater than sign to get this new set of steps

1/7 > 1/12

1*12 > 7*1

12 > 7

which leads us to a true statement. Therefore, 1/7 is the larger fraction and the more likely event.

Alternatively, you can use your calculator to find that:

Then for each decimal, move the decimal point 3 spots to the right. The values 0.143 and 0.083 become 143 and 83 respectively. We can see that 143 is larger, which means 0.143 is larger, and lastly 1/7 is larger. Think of it like a chain.