22. Probability

Question 1

P(event) =

Answer 1

number of ways to get a successful result / total number of ways of getting any result

Question 2

Range of P(E)

P(E) = pobability of E

Answer 2

0 ≤ P(E) ≤ 1

• P(E*) = 0 → impossible event
• P(E*) = 1 → certain event

Question 3

P(Ẽ)

set of outcomes not in E

Answer 3

P(Ẽ) = 1 – P(E)

Question 4

Disjunctive Probability

P (A ∪ B)

Answer 4

The probability of either A or B occuring.

P (A ∪ B) = P (A) + P (B) – P (A ∩ B)

Question 5

Conditional Probability

P (A | B)

Answer 5

The probability of A occuring, given that B has occured.

P (A | B) = P (A ∩ B) / P(B)

Question 6

Conjunctive Probability

P (A ∩ B)

when A and B are independent events

Answer 6

The probability of both A and B occuring.

P (A ∩ B) = P(A) • P(B)

Question 7

Mutually Exclusive

P (A ∪ B) = ?

Answer 7

Two events cannot both occur.

P (A ∪ B) = P(A) + P(B)

Note: P (A ∩ B) = 0