Probability and Patterns with Pascal



Probability and Patterns with Pascal

Ms. Miller

Due: Friday, September 28

Directions: In class, we had a discussion on Pascal’s triangle and how it is formed, but you have never seen a picture of it. Well now you will. Some of the values on the bulletin board of Pascal’s Triangle are incorrect. You need to put these values in their proper spots, and then fill out Pascal’s triangle on your worksheet by looking at the bulletin board. You will complete the worksheet on probability and patterns by using Pascal’s triangle. All work must be shown. The assignment will count as a 25 point homework grade. Do not forget the worksheet is due Friday, September 28 in class.

Note: You will need colored pencils for this activity. If there isn’t any available to you, please see me and I will let you borrow some!

Reminder: Scatter values after you place them in correct order!!!!

1. Put the values of Pascal’s triangle in their proper place and copy the values onto your worksheet in the space provided. Fill out the rest of the rows that were not on the bulletin board.

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2. What was the name of Pascal’s work which gave Pascal’s Triangle its name?

3. What is the triangle used for in mathematics that caused the triangle to be called Pascal’s triangle?

Probability and Pascal

Example: To find the probability of any boy-girl combination in a 5 child family.

~There are 5 children involved-look at the 5th row from the top.

~Total all the numbers in that row. There are 32 boy-girl combinations.

~The numbers at the end of the rows give the probability of the least likely combination (i.e. all girls or all boys). P(all boys) = P(all girls) = 1/32

~The middle number gives the most likely combination (i.e. probability of 2 girls and 3 boys or 3 girls and 2 boys). P(2 girls and 3 boys) = P(3 boys and 2 girls) = 10/32.

4. What is the probability of tossing a coin 8 times and getting all heads?

5. What is the probability of tossing a coin 5 times and getting 3 heads and 2 tails?

6. What is the probability of having a family of 9 girls?

7. What is the probability of having a family of 3 girls and 1 boy?

Patterns in Probability

8. Shade in all the multiples of 5. What pattern do you notice?

9. Find the sum of the numbers of each row. What pattern do you notice?

10. Find the rows that have prime numbers as their first element (remember the 0th element of every row is 1). Ignoring the one at the end of the row, what do you notice about every other element in that row?

EXTRA CREDIT (UP TO 4 POINTS): Find the Fibonacci Sequence in Pascal’s Triangle and illustrate it below.

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