Probability and Risk:

Question 1

What is introduced due to the complexity of living systems?

Answer 1

• Variability

- Uncertainty

Question 2

Why is it that risk is not always measured accurately?

Answer 2

Assessments of risk is bias- something that we are more familiar with appears to pose less threat and something less so appears to pose more.

Question 3

What is the difference between risk and probability?

Answer 3

Risk is the probability of something undesirable happening

Question 4

What is probability?

Answer 4

The proportion of times a particular outcome will occur from a large number of independent trials

Question 5

Why is the sample size so important when considering probability?

Answer 5

The proportion of times something happens will only accurately reflect the probability if there is a large number of independent trials

Question 6

What is the definition of the probability in relation to a single event?

Answer 6

The likelihood of getting a particular outcome from a single event

Question 7

What is probability denoted by?

Answer 7

𝑝

Question 8

What is the scale of probability?

Answer 8

0-1

Question 9

What does it mean if the probability of something happening is 0?

Answer 9

The event is will not happen, it is impossible

Question 10

What does it mean if the probability of an event happening is 1?

Answer 10

The event is going to happen, it is certain

Question 11

What does it mean that each trial/event is independent?

Answer 11

The outcome of one event/trial is doesn’t affect the probability of another

Question 12

When finding the probability of one or more independent events happening, what do you do with the probabilities?

Answer 12

Add them together

Question 13

What is 𝑝(A U B) equal to?

Answer 13

𝑝(A) + 𝑝(B)

Question 14

When is the equation 𝑝(A U B) = 𝑝(A) + 𝑝(B) valid?

Answer 14

When the A and B are mutually exclusive (where A and B represent outcomes)

Question 15

What does it mean that two events are mutually exclusive?

Answer 15

They cannot happen at the same time

Question 16

What do all mutually exclusive outcomes add up to?

Answer 16

1

Question 17

What is 1 - 𝑝(A U B) equal to?

Answer 17

𝑝(A U B)’

Probability of every mutually exclusive outcome but A and B

Question 18

What are probability distributions?

Answer 18

Graphical representations of theoretical probability of each outcome

Question 19

What is the independent and dependent variable between outcome and probability of outcome?

Answer 19

The possible outcomes is the independent variable and the probability of each outcome is the dependent variable

Question 20

Which axis do the dependent and independent variable go?

Answer 20

The independent variable goes on the x-axis and the dependent variable goes on the y-axis

Question 21

The area covered by the outcomes we are interested in within a probability distribution should be proportionate to what?

Answer 21

The probability of the outcome(s)

Question 22

What is 𝑝(A n B) equal to?

Answer 22

𝑝(A) x 𝑝(B)

Question 23

Under what condition is 𝑝(A) n 𝑝(B) = 𝑝(A n B)?

Answer 23

When the outcomes A and B are independent

Question 24

What is the difference between probability and frequency distribution?

Answer 24

Probability distributions refer to the theoretical probability of each outcome, whereas the frequency distribution refers to the observed frequency of each outcome (the experimental results)

Question 25

What can we do that will make the frequency distribution more similar to the probability distribution?

Answer 25

Increase sample size

Question 26

What is a binomial distribution?

Answer 26

A distribution involving only 2 different outcomes

Question 27

How can binomial distribution be used with probabilities involving more than 2 outcomes?

Answer 27

Group together all the possible outcomes into a fail or success category- where either category contains more than one outcome

Question 28

What can binomial distribution be used to calculate?

Answer 28

- Predict probability of success from a single experiment | - Predict the proportion of success from many repetitions

Question 29

How is binomial distribution calculated?

Answer 29

Probability of X number of successes in n number of trials

Question 30

𝑝(success) + 𝑝(failure)is equal to what?

Answer 30

1

Question 31

What denotes the probability of success?

Answer 31

p

Question 32

What denotes the probability of failure?

Answer 32

q

Question 33

Under what conditions does binomial probability work?

Answer 33

- Each trial is independent - Each trial has the same probability of success and failure - There is a large enough, fixed sample size (n> 50) - There are only two possible outcomes (success + failure)

Question 34

List the parameters used in binomial calculations:

Answer 34

- X = number of successes - size = number of trials - prob = probability of success in each trial - n = number of repeats - p = probability of overall outcome -

Question 35

What is the difference between number of trials and number of repeats?

Answer 35

Number of trials is the number of times an experiment is repeated to find the number of outcomes. Number of repeats is the number of time is trial is repeated

Question 36

List the functions needed to carry out distributions and probability in R:

Answer 36

- Binomial dbinom (x , size= , prob= ) - Cumulative probability pbinom (x , Size = , prob = ) - Normal distribution pnorm( X, mean = , sd = )

Question 37

What is the R function dbiom(X, size= , prob= ) used for?

Answer 37

Finding the probability density at each point

Question 38

When is the cumulative probability function used?

Answer 38

When we want to calculate the probability of getting a range of outcomes

Question 39

What does the function pbinom( X, size = , prob = ) calculate?

Answer 39

The cumulative probability density up to and including the stated number of success (X)

Question 40

What happens when you take discrete data, make a probability distribution and keep increasing the number of trials?

Answer 40

A normal distribution is formed

Question 41

What kind of distribution do continuous variables make?

Answer 41

Normal distribution

Question 42

How was normal distribution used in the past?

Answer 42

As an approximation for the binomial distribution

Question 43

How do you work out the probability of any particular outcome or range of outcomes once you know the probability distribution?

Answer 43

By finding the area under the curve

Question 44

List the parameters of Normal distribution:

Answer 44

- Mean (μ) | - Standard deviation (σ)

Question 45

What does the function pnorm(X, mean = , sd = ) carry out?

Answer 45

The cumulative probability density

Question 46

How do you work out what size group is required to be sure that two events are happening at the same time with cumulative binomial distributions?

Answer 46

By plotting the probability against number of outcomes