Week 2: Probability Theory

Question 1

MECE

Answer 1

Mutually Exclusive Collectively Exhaustive

Events cannot occur at the same time but one of the events must occur

Question 2

Factorials definition and denotation

Answer 2

n! = number of ways which n different objects can be places in order

Question 3

Permutations

Answer 3

number of different groups of r objects which can be chosen in order from n different objects

Question 4

Combinations

Answer 4

number of different groups of r objects which can be chosen from n different objects – order is irrelevant

Question 5

Pairwise mutually exclusive

Answer 5

used to describe a collection of events where no two events can occur simultaneously

Question 6

Probability of events:

• If A is impossible
• If B is certain
• If A is more likely than B

Answer 6

• If A is impossible P(A) = 0
• If A is certain P(A) = 1
• If A is more likely to occur than B P(A) > P(B)

Question 7

What does N denote?

Answer 7

total number of equally likely outcomes

Question 8

What does n denote?

Answer 8

The number of these elementary outcomes that are favourable to our event in interest

Question 9

Permutation Equation

Answer 9

Question 10

Combinations formula

Answer 10

Question 11

What is the equation associated with relative frequency?

Answer 11

Question 12

3 axioms of event probability

Answer 12

1. for any event A, P(A) >/= 0
2. for the sample space S, P(S) = 1
3. If {A(i)}, i - 1,2…n are mutually exclusive events

Question 13

Probability of mutually exclusives union

Answer 13

Sum of their respective probabilities

Question 14

Symbol of Union

Answer 14

U

Question 15

Meaning and Symbol of Intersect

Answer 15

∩ - and

Question 16

Meaning and Symbol of ‘Complement of’

Answer 16

∁- Complement of a set is the set that includes all the elements of the universal set that are not present in the given set

Question 17

What does the addictive law state?

Answer 17

So P(A ∪ B) is the probability that at least one of A and B occurs and P(A ∩ B) if the probability that both A and B occur

Question 18

The Multiplicative Law

Answer 18

The probability of occurrence of both events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs

Question 19

Baye’s Formula (simplest form)

Answer 19

Question 20

Total Probability Equation

Answer 20

Question 21

Bayes Formula - General form

Answer 21

Question 22

When are two events A and B independent?

Answer 22

if and only if: