Topic 2 (Part 2)

Question 1

is the science determining how likely an event occur

Answer 1

Probability

Question 2

any game of chance that led to
the early development of
probability theory

Answer 2

Gambling

Question 3

Branches of Probability

Answer 3

• Weather Forecasting
• Business
• Politics
• Scientific Research

Question 4

two or more events that have no common outcomes are said to cannot occur simultaneously

Answer 4

Mutually Exclusive

Question 5

Applies to union of events

If A and B are two events, then
𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 ∩ 𝐵)

Answer 5

Additive Rule

Question 6

If A and B are mutually exclusive, then
𝑃 𝐴 ∪ 𝐵 = 𝑃 (𝐴 ) + 𝑃 (𝐵)

Answer 6

Rule

Question 7

For three events A, B, and C,

𝑃 (𝐴 ∪ 𝐵 ∪ 𝐶) = 𝑃 (𝐴) + 𝑃 (𝐵) + 𝑃 (𝐶) − 𝑃 (𝐴 ∩ 𝐵) − 𝑃 (𝐴 ∩ 𝐶) − 𝑃 (𝐵 ∩ 𝐶) + 𝑃 (𝐴 ∩ 𝐵 ∩ 𝐶)

Answer 7

Rule

Question 8

the probability of an event B occurring when it is
known that some event A has occurred and denoted as,

𝑃 (𝐵|𝐴) = 𝑃(𝐴 ∩ 𝐵) / 𝑃(𝐴), 𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 𝑃 (𝐴) > 0

Answer 8

Conditional Probability

Question 8

If A and A’ are complementary events, then

𝑃 (𝐴) + 𝑃 (𝐴′) = 1

Answer 8

Rule

Question 9

Two events A and B are independent if and only if 𝑃 (𝐵|𝐴) = 𝑃 (𝐵), 𝑜𝑟 𝑃 (𝐴|𝐵) = 𝑃 (𝐴)
assuming the existences of the conditional
probabilities. Otherwise, A and B are dependent

Answer 9

Independent Events

Question 10

If in an experiment the events A and B can both occur, then
𝑃 (𝐴 ∩ 𝐵) = 𝑃 (𝐴) 𝑃 (𝐵|𝐴), 𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 𝑃 (𝐴) > 0

Answer 10

Product Rule

Question 11

If the events B1, B2, …, Bk constitute a partition of the sample space S such that P(Bi) ≠ 0 for i = 1, 2, …, k, then for any event A in S such that P(A) ≠ 0

Answer 11

Bayes’ Rule