Sequences 4: Pascal's Triangle
http ://www. youtube. com/watch? v=bMB8qD Ya8N 0
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What do you know about Blaise Pascal? What do these terms mean?
exponent coefficient variable binomial expansion
Listen to and watch the video, answer questions and fill in the missing items.
a) What is the aim of the lecture?.........................................................
b) We need to recognize the relations between.........................................
c) The first and the last terms are both raised to................................
d) Whatever exponent I start with on the variable it...............from that exponent down
to an exponent of...........The other exponent...............from zero up to x to the nth
power.
e) The first and last.................arel.
f) The so called binomial expansions keep you from......................................
g) You add two numbers above to get.......................................................
h) Pascal was a.................................................................................
i) If you know Pascal's triangle, you can..................................................
j) If you add up............of Pascal's triangle, you get the Fibonacci sequence.
k) What does the speaker like about maths?....................................................
Pascal' s Triangle
Adaptedfrom Nucleus, Maths, English for Science and Technology
1) Read the text and fill in the missing words. Try to guess.
A single dice is thrown. There are two possible outcomes - odd or.........The chances of
throwing an odd number are 1 in 2, and so are the.........of throwing an even number.
Supposing now that two.......are thrown. There are now three possible outcomes: both odd,
both even, or one odd and one even. But the last result, one odd and one even, can occur in
two different ways, either the........dice odd and the second dice even, or the first dice even
and the second dice odd. So the chances of throwing.......odd are 1 in 4 of throwing both
even 1 in 4, and of throwing one odd and one even 2 in 4. Throwing three dice produces.......
different possibilities: EEE, EEO, EOO, EOE, OEE,.......OOE and OOO. Thus the
probabilities are as follows: all evens, 1 in 8, all odds 1 in 8, two odds and one even,.... in 8, two evens and one......, 3 in 8.
These results can be..........by using a device called Pascal's Triangle, the first three
rows of which are shows in Fig. 10.1. This triangle can easily be formed. The first and last
figure in each row is.......Every other figure is the.......of the two figures above it. Thus, in
the second row, 2 is the sum of 1 and 1. In the third row, both threes are formed by.........2
and 1. The total of all figures in each row gives the total number of possibilities for that row. Thus the third row has 1+.. ,+3+1 possibilities.
2) Write down the next three rows of Pascal's triangle
1 1 1     2 1 13      3 1
Using the triangle, state the chances of the following events when throwing six dice.
a) All odd
b) Either all odd or all even
c) An equal number of odd and even
d) Five odd and one even or vice versa