ASB Week 8 Practice

ASB Week 8 Math Practice

• Events with two outcomes

• Binomial expansion

Events with Two Outcomes

Examples

• Flipping a Coin

• Male/Female

How to solve:

Multiple Choice

EXAMPLE: If four coins are flipped, what is the probability of getting two heads and two tails?

• $$\frac{3}{8}$$

• $$\frac{1}{4}$$

• $$\frac{5}{16}$$

• $$\frac{1}{2}$$

Multiple Choice

YOU TRY: If three coins are flipped, what is the probability of getting one heads and two tails?

• $$\frac{3}{4}$$

• $$\frac{3}{8}$$

• $$\frac{5}{8}$$

• $$\frac{7}{16}$$

Binomial Expansion w/ Pascal's Triangles

​Definition

• Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)ⁿ, where n is the row of the triangle.

• The Binomial Theorem tells us we can use these coefficients to find the entire expanded binomial, with a couple extra tricks thrown in.

Multiple Choice

EXAMPLE: When $$\left(x+1\right)^4$$ is expanded, the fourth term is ______.

• 1

• 4

• 6

• 3

Multiple Choice

YOU TRY: When $$\left(x+1\right)^5$$ is expanded, the third term is ______.

• 5

• 10

• 6

• 1

Multiple Choice

EXAMPLE: When $$\left(2x-1\right)^3$$ is expanded, the second term is ______.

• $$-6x^2$$

• $$3x^2$$

• $$6x^2$$

• 1

Multiple Choice

EXAMPLE: When $$\left(3x-1\right)^4$$ is expanded, the second term is ______.

• $$-12x^3$$

• $$12x^3$$

• $$4x^3$$

• 1

Multiple Choice

EXAMPLE: There are 7 terms in the expansion of $$\left(3x-y\right)^{2n}$$ .  Determine the value of n.

• 3

• 6

• 12

• 7