IAL Edexcel S2 Binomial Distribution

IAL S2 Binomial Distribution

Discrete Probability Distribution!
Identifying the number of Successes
In 'n' independent trials!

Multiple Choice

The variable used for the number of trials.

• n

• x

• p

• q

Multiple Choice

The variable used for the number of success.

• s

• x

• p

• q

Multiple Choice

The variable used for the probability of success.

• s

• x

• p

• q

Multiple Choice

What does 4! equal to?

• 24

• 120

• 4

• 20

Multiple Choice

If p=0.65, what does 'q' equal to?

• 0.35

• 0.65

• 1

• 0.45

Multiple Choice

What was the name of Miss Davidson/Mrs Yeldham’s first Golden Retriever?

• Willow

• Bonny

• Pepper

• Simba

Multiple Choice

Which celebrity owns three golden retrievers named Luke, Layla and Gracie?

• Beyonce

• Brad Pitt

• Oprah

• Drake

Multiple Choice

Which film has a golden retriever named Shadow?

• 101 Dalmations

• Lady and the Tramp

• Air Bud

• Homeward Bound

Fill in the Blanks

Multiple Choice

If asked 3 of these questions, where the probability of success is 0.25, which notation represents this distribution?

• $$X=B\left(3,\ 0.25\right)$$  

• $$X\sim P\left(3,\ 0.25\right)$$

• $$X\sim B\left(0.25,\ 3\right)$$  

• $$X\sim B\left(3,\ 0.25\right)$$  

Multiple Choice

If asked 3 of these questions, how many ways are there of answering 2 correct?

• 3 

• 2

• 6 

• 1 

Multiple Select

If asked 3 of these questions, how many ways are there of answering 3 correct?

• 3 

• 2

• 6 

• 1 

Multiple Select

If asked 10 of these questions, how many ways are there of answering 8 correct?

• $$10C_8$$  

• $$10C_2$$

• $$8C_2$$  

• $$8C_{0.25}$$  

Multiple Select

How many ways are there of arranging 5 different coloured beads in a line?

• 5 x 4 x 3 x 2 x 1

• 5

• 5C5

• 5!

Multiple Select

How many ways are there of arranging 2 red beads and 3 blue beads in a line?

• 5 x 4 x 3 x 2 x 1

• 5C2

• 5C3

• 3 x 2

Multiple Select

I throw a coin 8 times. How many possibilities are there in which I threw 4 Heads?

• 4 x 3 x 2 x 1

• 8C4

• $$\frac{8!}{4!4!}$$

• 4!

Multiple Select

If you have 8 people at a dinner table, how many ways are there for 6 of them to be left-handed?

• $$\frac{8!}{6!2!}$$  

• 8C2

• 8C6

• 8!

Multiple Select

How many ways of arranging 4 red balls, 3 green balls and 2 blue balls in a line?

• $$\frac{9!}{4!3!2!}$$  

• 9C4

• 9C3

• 9C2

Multiple Choice

X~B(12, 1/6)

• n=12, p=1/6

• p=12, n=1/6

• 12 trials, probability of failure is 1/6

• 6 trials, probability of success is 1/6

Multiple Choice

X~B(12, 1/6)

What is P(X=2)?

• 0.296

• 0.926

• 0.962

• 0.629

Multiple Choice

X~B(12, 1/6)

What is P(X≤1)?

• 0.296

• 0.704

• 0.112

• 0.381

Multiple Choice

I have a bag of 2 red and 8 white balls. X represents the number of red balls I chose after 5 selections (with replacement). How is X distributed?

• $$X\sim B\left(8,\ \frac{2}{10}\right)$$  

• $$X\sim B\left(10,\ \frac{2}{10}\right)$$  

• $$X\sim B\left(5,\ \frac{8}{10}\right)$$  

• $$X\sim B\left(5,\ \frac{2}{10}\right)$$  

Multiple Choice

I have a bag of 2 red and 8 white balls. X represents the number of red balls I chose after 5 selections (with replacement). Determine the probability that I chose 3 red balls.

• 0.512

• 0.0512
  

• 0.205

• 0.025

Cumulative Distribution Function 

• F(x)=P(X≤x)

• “the probability of the outcome being up to a particular value”.

• Imagine being asked for P(X≤9)

• = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)

• Boring! and way too time consuming....

Cumulative Distribution Function 

• Lets look at the random variable X~B(20,0.4) 

• Turn to page 17 in your formula booklet

• Find the box where n=20

• ​Find where p=0.4 in the top row

• ​This column will give you any answers you need.

• ​Find P(X≤7)

Open Ended

X~B(20,0.4)

What do you think P(X≤7) is?

Open Ended

X~B(20,0.4)

What do you think the P(X<6)=

Open Ended

X~B(20,0.4)

What do you think the P(X≥15)=

Open Ended

In part (a) why did I subtract 0.3783?

Open Ended

In part (b) why is 1 the WRONG answer?