Since it is my birthday today, I wanted to provide you with a birthday themed quiz. Test your knowledge by seeing how well you do. Enjoy and good luck!

### 1. Suppose that I am in a classroom with 25 other people. What is the probability that someone other than me will also have their birthday today?

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The actual probability that someone will have the same birthday is \(1-\left(\frac{364}{365}\right)^{25} \approx .066\) or \(6.6\%\).

### 2. Suppose that I am in a classroom with 25 other people. What is the probability that 2 of the students share the same birthday?

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The actual probability that someone will have the same birthday is \(1-\left(\frac{P(365,25)}{365^{25}}\right) \approx .569\) or \(56.9\%\).

### 3. You have two pieces of cardboard that are 12 inches by 18 inches. For each piece, you will cut a square out of the corners. You will then fold the carboard in order to make a rectangular solid with no top (or bottom depending on perspective). By placing the two on top of each other you will create a box to put a present in. What length should you cut out of the corners in order to maximize the volume of the box?

inches.Click to submit answer.

The side of the square you should cut out would be \(5-\sqrt{7} \approx 2.35\)inches. This would result in a box with volume \(228.16\text{in}^{3}\).

### 4. Suppose that I brought cake to class. For the cake, there are 10 pieces of chocolate cake, 8 pieces of white cake, and 7 pieces of carrot cake for the students to share. How many distinct ways can I distribute these pieces of cake to the 25 students?

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There are \(\frac{25!}{10!8!7!}\approx 21\)billion ways to do this.

### 5. Currently I am \(n\) years old. We have the following \[\begin{align*} n &\equiv 0 \text{mod} 2 \\ n& \equiv 1 \text{mod} 3 \\ n & \equiv 4 \text{mod} 5\end{align*}\] and \(10 \leq n \leq 60\). How old am I?

I am years old.Click to submit answer.

I am 34 years old.

### Number correct 0/5.

Thank you for working on the quiz. I hope you enjoyed it and did very well. If you enjoyed the quiz, check out my other birthday post so that you can see how you can support STEM and leaf!