Probability General Ideas

Question 1

Definition of independent events?

Answer 1

Two events, A and B, are independent if the occurrence of one does not affect the probability of the other occurring.

Question 2

P(A and B) of independent events?

Answer 2

P(AandB) = P(A) × P(B)

Question 3

Events A and B are independent if . . .

Answer 3

P(A and B) = P(A) × P(B)
P(A | B) = P(A)
P(B | A) = P(B)

Question 4

Definition of dependent events?

Answer 4

Two events, A and B, are dependent if the occurrence of one event affects the probability of the other. Commonly, P(B∣A) represents the probability of B given that A has occurred.

Question 5

P(A and B) of dependent events?

Answer 5

P(A and B) = P(B ∣ A) × P(A)

Question 6

Definition of mutually exclusive events?

Answer 6

Two events, A and B, are mutually exclusive (or disjoint) if they cannot both occur at the same time.

Question 7

P(A and B) of mutually exclusive events?

Answer 7

P(AandB) = 0

Question 8

P(AorB) of mutually exclusive events?

Answer 8

P(AorB) = P(A) + P(B)

Question 9

Definition of non-mutually exclusive events?

Answer 9

Two events, A and B, are non-mutually exclusive if they can both occur at the same time.

Question 10

P(AorB) of non-mutually exclusive events?

Answer 10

P(AorB) = P(A) + P(B) − P(AandB)

Question 11

Definition of conditional probability?

Answer 11

The probability of one event occurring given that another event has already occurred.

Question 12

P(B given that A)?

Answer 12

P(B∣A) = P(AandB) / P(A)
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Question 13

What is Baye’s Theorem for P(B∣A)?

Answer 13

P(B∣A) = P(A∣B )× P(B) / P(A)
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Question 14

P(A given that B)?

Answer 14

P(A∣B) = P(AandB) / P(B)

Question 15

When working conditionally it is sometimes easier to calculate P(A and B) as . . .

Answer 15

P(A|B) ⋅ P(B) OR P(B|A) ⋅ P(A)

Question 16

Can events be independent and mutually exclusive?

Answer 16

NO unless one of the events has a zero probability (i.e., one of the events cannot occur). This is because mutually exclusive events can never occur together, whereas independent events can.

Question 17

When asked for P(A or B) of independent events?

Answer 17

P(AorB) = P(A) + P(B) − P(AandB)
Because independent events are NOT mutually exclusive

Question 18

Addition Rule for . . .
Mutually Exclusive Events:
Non-Mutually Exclusive Events:

Answer 18

Mutually Exclusive Events:
P(AorB) = P(A) + P(B)

Non-Mutually Exclusive Events:
P(AorB) = P(A) + P(B) − P(AandB)

Question 19

Multiplication Rule for . . .
Independent Events:
Dependent Events:

Answer 19

Independent Events:
P(AandB) = P(A) × P(B)

Dependent Events:
P(AandB) = P(A) × P(B∣A)