WK 1 Part 2 PSY115

Question 1

When is it ok to add probabilities?

It is only ok to add probabilities of events if it is impossible for both events to happen at the same time.

Example of bad reasoning:
The chance of rolling an even number on a six-sided die is 50%. The chance of rolling a number greater than or equal to 4 is 50%. Therefore the chance of rolling a number that is even OR greater than or equal to 4 is 100%. THIS IS WRONG.

–The reason this doesn’t work is that we have double counted 4 and 6.

Answer 1

X

Question 2

When is it ok to MULTIPLY probabilities?

It is only ok to multiply probabilities of events if they are INDEPENDENT.

Events are independent if one event happening does not influence the probability of the other event happening

Example of BAD reasoning:
The chance of rolling an even number on a six-sided die is 1/2. The chance of rolling a number greater than or equal to 4 is 1/2. Therefore the chance of rolling a number that is even AND greater than or equal to 4 is ½×½=¼. WRONG.

Answer 2

X

Question 3

Misunderstanding of how to work with probabilities can have nasty consequences
–The Sally Clark case
–“[Meadow] stated in evidence as an expert witness that “one sudden infant death in a family is a tragedy, two is suspicious and three is murder unless proven otherwise” (Meadow’s law). He claimed that, for an affluent non-smoking family like the Clarks, the probability of a single cot death was 1 in 8,543, so the probability of two cot deaths in the same family was around “1 in 73 million” (8543 × 8543). Given that there are around 700,000 live births in Britain each year, Meadow argued that a double cot death would be expected to occur once every hundred years.”
- source https://en.wikipedia.org/wiki/Sally_Clark

Answer 3

X

Question 4

In mathematics, true statements are called THEOREMS

These are statements whose truth you can prove using logic.

The proof requires starting from a few basic statements, called AXIOMS.

Answer 4

X

Question 5

The equation consists of four parts and here’s the traditional terminology for each term:

P(Event-1): Prior probability

P(Event-2): Evidence

P(Event-2 | Event-1): Likelihood

P(Event-1 | Event-2): Posterior probability

Answer 5

X