Probability

Question 1

What is probability?

Answer 1

Probability is the likelihood of an event occurring.

Question 2

What is an event?

Answer 2

An event is the outcome of a given experiment.

Question 3

What is an experiment?

Answer 3

An experiment is any statistical process which generates outcomes.

Question 4

What is a trial?

Answer 4

A trial is a random experiment resulting in random outcomes.

Question 5

What is sample space?

Answer 5

Sample space is a set of all possible outcomes of a given experiment.

Question 6

What is the addition rule for probability?

Answer 6

P(A or B) = P(A) + P(B) - P(A n B)
But if A and B are mutually exclusive outcomes, then the formula becomes:

P(A or B) = P(A) + P(B)

Because P(A n B) is zero.

Question 7

If A and B are mutually exclusive and collectively exhaustive, what can be said about “collectively exhaustive”, and P(A) and P(B)?

Answer 7

Collectively exhaustive means the events (here, A and B) cover the entirety of the sample space of the experiment – no other event or alternative outcome exists.

That said, the above conditions imply that:
P(A) + P(B) = 1

Question 8

What is the multiplication rule of probability?

Answer 8

P(A n B) = P(A) × P(B|A)
Or = P(B) × P(A|B)
Where ‘|’ means ‘given that __ has occurred.
If A and B are independent, then:
P(A n B) = P(A) x (B)

Question 9

How to tell when a distribution is Binomial?

Answer 9

BINS; the distribution must have:
1. Binary Outcomes
2. Independent events (outcome of first does not affect the outcome of the others.)
3. Number of trials must be multiple
4. Same probability for all outcomes, as in the roll of a die and the toss of a coin.

Question 10

What is Poisson Distribution?

Answer 10

Poisson distribution estimates the number of times (frequency) of a random independent event occurring over a period of time or a stretch of space.

Question 11

What is the formula for probability of a Poisson distribution?

Answer 11

P(x) = λ^x • e^–λ / x!