Probability: Binomial Distribution 1

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Ben McGovern

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Ruth Hand

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Ready to use

3 years, 8 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

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Ruth Hand 3 years, 8 months ago

Gave some feedback: Ready to use

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Ben McGovern 4 years, 3 months ago

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Name	Status	Author	Last Modified
Probability: Binomial Distribution 1	Ready to use	Ben McGovern	27/09/2022 09:01
Binomial Distribution 2	Ready to use	Ben McGovern	27/09/2022 09:01

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Question statement

A teacher has a small class of 4 students. On any given day there is a probability of $\var{prob}$ that they will be asked a question by a student.

The event of a student asking a question is independent of whether or not any other student asks a question.

Give any introductory information the student needs.

			Name	Type	Generated Value

prob	number	0.4
n	integer	3
sol2	number	0.1792
sol1	number	0.0256
partb	string	<p>If the teacher is asked que
b1	string	<p>If the teacher is asked que
b2	string	<p>If the teacher is asked que

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.1..0.4 #0.1)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

0.4

→ Used by:

b1
b2
sol1
sol2

Statement
Advice

Parts

Information only
Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Information only

Ask the student a question, and give any hints about how they should answer this part.

Find the probability that on a particular day,

Advice

The answers involve binomial distributions because there are only 2 cases - a student either asks a question or they do not.

Therefore, we want to apply the binomial distribution

$P(X=r) =\, ^nC_r \, p^r \, (1-p)^{n-r}.$

Let $X$ be the number of students who ask a question.

Part (a):

$\begin{split} P(X=4) &\,= \binom{4}{4} \times \var{prob}^4 \times \var{1-prob}^0 \\ &\,= \var{prob}^4 \\ &\,= \var{sol1}. \end{split}$

Part (b):

{partb}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 8 months ago

Ben McGovern 4 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Information only

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Probability: Binomial Distribution 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 8 months ago

Ben McGovern 4 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Information only

Generated value: `number`