Seventy balls numbered from 1 to 70 are placed in an urn. One ball is randomly drawn from the urn. What is the probability that the number on the ball is greater than or equal to 30?

Hey there! I'm happy to help!

We know that there are seventy balls in the urn...

We are looking for the probability that the one we choose is greater than or equal to thirty...

So, this means that we can pick 30, 70, and any number in between. How many numbers are in between thirty and seventy, though? Well, you might be tempted to say forty, but we have already counted 30 and 70. Given that information, you might just want to subtract two, but it's important to note that including 30 and 70, there are 41 balls. Why?

Well, if it had to be greater than thirty, we would have 40 possible balls. In our case, 30 would kind of be counted as a zero if you were counting on a number line. If you had 20 balls and took and took away ten, you would have 10 balls left. This means that if you start at twenty and go backwards, THEN you have ten. If you don't count twenty, there are nine in between. If ten is included, then we would have 11! Pretty confusing, right? Math is weird, but you'll get the hang of it!

So, how many numbers are in between 30 and 70? Well, it would be 49 given our other examples. If you ask how many numbers are between 0 and 10, it's nine! We just apply it on a bigger scale. But, we also have to add  our ball with 30 and our ball with 70. This means that we have 51 balls that are greater than or equal to 30.

We can now put this probability out of 70 in fraction, decimal, and percent form. To find the fraction, put what we want over the total. For the decimal, divide the numerator by the denominator of the fraction. For the percent, multiply the decimal by 100 and put a percent sign!

Fraction: 51/70

Decimal: 0.73 (to the nearest hundredth)

Percent: 73%

I hope that this helps! Have a wonderful day!

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