Topic 6: Sampling Data

Question 1

Explain The Prosecutor’s Fallacy

Answer 1

The Prosecutor’s Fallacy happens when it is assumed that the probability of innocence given that the evidence matches is equal to the probability of evidence matches given the innocence.

Actually, it is not equal.

Question 2

Explain chance and sample space

Answer 2

• Chance is the probability of an event is likely to occur if the process if repeated on long term.
• Sample space is ALL the possible outcomes of an event

Question 3

Explain conditional probability

Answer 3

• Conditional probability is the chance that an event occurs given that another event has occured.

Question 4

Explain independence, dependence, and how multiplication principle is applied in both cases

Answer 4

• Independence is when the occurence of event 1 doesn’t change the chance of event 2
  + P(event 2|event 1) = P(event 2)
  + sampling with replacement
• Dependence is when the occurence of event 2 is dependent on event 1
  + sampling without replacement
• Multiplication principle is applied when both events occur
  + Indepedent: P(event 1)P(event 2)
  + Dependent: P(event 1)P(event 2|event 1)

Question 5

Explain mutually exclusive events and how additional principle is applied

Answer 5

• 2 events are mutually exclusive is when the occurence of 1 event PREVENTS the occurence of the other one.
• Additional principle is applied when at least 1 of 2 events occur
  + P(at least 1 of 2 events occur) = P(event 1) + P(event 2)

Question 6

When is factorial used?

Answer 6

Factorial is used to figure out the number of ways arranging n distinct objects in a row

Question 7

What is binomial coefficient?

Answer 7

Binomial coefficients calculate the number of ways arranging n objects of 2 types (x and n-x) in a row.
Or the number of ways we can pick a combination of x objects out of n objects

\binom {n}{k}=\frac {n!}{k!(n-k)!}

Question 8

What is binary trial?

Answer 8

Binary trial is when ONLY 2 outcomes/things can occue
P(event) = p and P(not event) = 1-p

Question 9

Describe the binomial theorem

Answer 9

Binomial Theorem is the probability of exactly x events occur in n independent, binary trials given the probability of event occuring is p

(n chooses x)p^x(1-p)^(n-x)