Mar 30, 2020 | High Park

Have fun solving these puzzles this week mathletes!

**Lower Elementary:**

*Question: *Martin rolls a fair, standard, six-sided die. Match each outcome with its likelihood.

• Martin rolls an even number. |
• Impossible |
---|

**Upper Elementary:**

*Question: *Tara gets to draw one bill at random from either of two buckets. One bucket has 30 $1 bills and 2 $100 bills. Another bucket has 80 $1 bills and 4 $100 bills. Which bucket should Tara choose? Why?

**Middle School:**

*Question: *The ratio of apples to oranges in a box is 7:18. What is the percent chance that a fruit drawn at random from the box will be an orange?

**Algebra and Up:**

*Question: *There are 100 marbles in a bag. They’re numbered 0, 1, 2, all the way through 99. What is the probability that if you draw three marbles out of the bag at random without replacing them, the number on the first marble will be 0, the number on the second will be 1, and the number on the third will be 2?

...

__Answers:__

**Lower Elementary:**

*Question: *Martin rolls a fair, standard, six-sided die. Match each outcome with its likelihood.

• Martin rolls an even number. |
• Impossible |
---|

*Solution: *It’s as likely as not that Martin rolls an even number because there are 3 even numbers and 3 odd numbers on a die. It’s impossible that he rolls an 8 because there isn’t an 8 on a die. It’s certain that he rolls a number less than 10 because all the numbers on a die are less than 10. It’s unlikely that he rolls a 1 because only 1 out of 6 numbers on a die is 1. It’s very likely that he doesn’t roll a 6 because 5 out of 6 numbers on a die aren’t 6.

**Upper Elementary:**

*Question: *Tara gets to draw one bill at random from either of two buckets. One bucket has 30 $1 bills and 2 $100 bills. Another bucket has 80 $1 bills and 4 $100 bills. Which bucket should Tara choose? Why?

*Answer: *Tara should choose the bucket with 30 $1 bills and 2 $100 bills.

*Solution: *Since 2 out of 30 + 2 = 32 bills in the first bucket are $100 bills, that means that ^{2}/_{32} = ^{1}/_{16} of the bills are $100. In the other bucket, 4 out of 80 + 4 = 84 bills are $100, so ^{4}/_{84} = ^{1}/_{21} bills are $100. Since the first bucket has the greater fractional part comprising $100 bills, that’s the smarter bucket to choose.

**Middle School:**

*Question: *The ratio of apples to oranges in a box is 7:18. What is the percent chance that a fruit drawn at random from the box will be an orange?

*Answer: *72%

*Solution: *There are 7 + 18 = 25 fruits in the box. Since 18 out of 25 fruits are oranges and a percentage is out of 100, we can multiply 18 and 25 each by 4 to find the number of fruits out of 100 that are oranges. 18 × 4 = 72, so 72% of the fruits are oranges. If one is chosen at random, then the percent chance that it’ll be an orange is 72%.

**Algebra and Up:**

*Question: *There are 100 marbles in a bag. They’re numbered 0, 1, 2, all the way through 99. What is the probability that if you draw three marbles out of the bag at random without replacing them, the number on the first marble will be 0, the number on the second will be 1, and the number on the third will be 2?

*Answer: *1 out of 970,200

*Solution: *The probability of drawing the 0 first is ^{1}/_{100}. If the marble isn’t replaced, then the probability of drawing the 1 next is ^{1}/_{99}. Then, the probability of drawing the 2 next is ^{1}/_{98}. So, the probability of drawing exactly those numbers in that order is ^{1}/_{100 × 99 × 98} = ^{1}/_{970,200}.