Topic 6 - Understanding Chance

Question 1

L.O.

Answer 1

LO6 Use the box model to describe chance and chance variability, including sample surveys and the central limit theorem

Question 2

The Prosecutors Fallacy

Answer 2

Is a mistake in statistically thinking.
Whereby its assumed that the probability of a random match is equal to the probability that the defendant is innocent.
Used in court as an argument for/ against defendants.

Question 3

Binary trials

Answer 3

When there are 2 possible outcomes
(Yes/No)
(Heads/Tails)

Question 4

Properties of chance

Answer 4

Chance is the percentage of time a certain event is expected to happen, if same process of repeated long-term
Basic properties:
1. Chances are between 0-100%
2. Chance of something = 100% - complement event
3. Drawing at random means every choice has an even chance of being picked

Question 5

Conditional probability and multiplication principle

Answer 5

Conditional Probability:
- The chance that a certain event occurs, given another event has occured

Multiplication Principle:
- The probability that 2 events occur is the chance that the chance of the 1st event multiplied by the chance of 2nd event, given the 1st event has occured

Question 6

Independance

Answer 6

Two Events are independant if the chance of the 2nd given the first is the same as the second

• Drawing randomly with replacement ensures independance

Question 7

Dependance

Answer 7

• Two events are dependant if the chance of the 2nd given the 1st is not the same as the chance f the 2nd as it depends on the result of the 1st event
• Drawing without replacement ensures dependance

Question 8

Mutually exclusive Vs Independance

Answer 8

Mutually excl:
- Two things are mutually exclusive when the occurance of one event prevents the other
- Occurance of event 1 prevents event 2 occuring

Indep:
Occurance of event 1 does NOT chance the chances of event 2.

Question 9

Making lists…

Answer 9

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Question 10

Addition rule

Answer 10

If 2 things are mutually exclusive, then the chance of at least 1 occuring is the sum of the individual chances
- The probability that at least one of the 2 events occur

• Applies if the data is mutually exclusive

Question 11

Binomial coefficients

Answer 11

Factorial:
- The number of ways rearranging n distinct objects in a row is n factorial.
- n!

Binomial coefficient:
- Suppose there are n objects in a row, made up of x number of 1 and n-x of 2.
- The number of ways of rearranging the n objects is given by the binomial coefficient:
(n x) = n!/ (x!(n-x)!)

Question 12

Binomial theorum

Answer 12

Suppose we have n independant, binary trials, with P(event) = p at every trial, and n is fixed.
The chance that exactly x events occur is:
(n x)p^x (1-p)^(n-x)

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Question 13

Binomial theorum example

Answer 13

A fair coin is tossed 5 times. What is the probability of getting 3 heads?

Working:
x= 3, n= 5, p= 0.5

(5 3) 0.5^3 (1-o.5)^(5-3)
= 0.3125