Binomial distribution Binomial Formula and Pascals triangle

Open Ended

What makes the colour blindness experiment a binomial distribution?

Open Ended

Explain why drawing marbles without replacement does not fit a binomial distribution.

Multiple Choice

Which probability experiments from Exercise 14D can be modeled by a binomial distribution?

• a, b, c

• a, b, d

• a, c, d

• b, c, e

Multiple Choice

What is the probability that all 10 men in a random sample are colour blind, given that colour blindness affects about 8% of men?

• (0.08)^10

• (0.92)^10

• (0.08)^2 × (0.92)^8

• 10 × (0.08)^2 × (0.92)^8

Open Ended

Explain how the probability that no men in a random sample of 10 are colour blind is calculated using the binomial distribution formula.

Multiple Choice

Which of the following expressions correctly represents the probability that exactly 2 men out of 10 are colour blind?

• (0.08)^2 × (0.92)^8

• 10 × (0.08)^2 × (0.92)^8

• 45 × (0.08)^2 × (0.92)^8

• (0.08)^10

Multiple Choice

What is the probability that exactly two men are colour blind, based on the given probability values?

• 0.148

• 0.08

• 0.92

• 0.45

Multiple Choice

In the binomial probability formula P(X = 2) = 10C2(0.08)^2(0.92)^8, what does 10C2 represent?

• The number of ways to choose 2 colour blind men from 10.

• The probability of success.

• The probability of failure.

• The total number of men.

Open Ended

Explain how the binomial coefficient is used to determine the number of ways two men can be colour blind in a group of ten.

Open Ended

How does Pascal's Triangle help in expanding binomial expressions such as (2 + x)^4?

Multiple Choice

Which of the following statements about Pascal's Triangle is correct?

• Each term is the sum of the two terms above it.

• The second number in each row is always 2.

• Pascal's Triangle only applies to binomial expansions.

• The first row always contains only 1s.

Open Ended

Write down the first 6 rows of Pascal's triangle.

Open Ended

Explain how Pascal's triangle can be used to find the number of combinations for a given selection.

Multiple Choice

Which value in the 5th row of Pascal's triangle represents the number of ways to choose 3 items from 5? 5C3

• 5

• 10

• 15

• 20

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Multiple Select

Select all rows in Pascal's triangle that can be used to calculate combinations for n = 6.

• Row 1

• Row 3

• Row 6

• Row 5

Multiple Choice

Which calculator function is used to find combinations for larger values of n?

• nPr

• nCr

• Sum

• Matrix

Open Ended

Use your GDC to calculate the following values

Open Ended

Multiple Choice

X ~ B(20, 0.5)

Find P(X ≤ 7)

• 0.07

• 0.13

• 0.87

• 0.94

Open Ended

What do you see?

Open Ended

What are some real-life situations where you could use the Binomial Distribution to calculate probabilities?