Probability

Question 1

probability of an event A

Answer 1

P(A)= Totalnumberofoutcomes /Numberoffavorableoutcomes

Question 2

Complement Rule

Answer 2

P(A^c )=1−P(A)

Question 3

Addition Rule (for two events)

Answer 3

P(A∪B)=P(A)+P(B)−P(A∩B)

Question 4

If A and B are mutually exclusive

Answer 4

P(A∪B)=P(A)+P(B)

Question 5

Conditional probability

Answer 5

P(A∣B)= P(A∩B)/P(B)
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Question 6

If events are Independent

Answer 6

P(A∩B)=P(A)⋅P(B)

Question 7

Bayes’ Rule

Answer 7

P(A∣B)= [P(B∣A)⋅P(A)]/P(B)

Question 8

Permutations (order matters)

Answer 8

P(n,r)= n!/(n−r)!

Question 9

Expected value (discrete)

Answer 9

E(X)=∑x⋅P(x)

Question 10

Variance (discrete)

Answer 10

Var(X)=E(X ^2)−[E(X)] ^2

Question 11

Probability (continuous)

Answer 11

P(a≤X≤b)=∫f(x)dx

Question 12

Expected value (continuous)

Answer 12

E(X)=∫ xf(x)dx
between infinity and negative infinity

Question 13

Variance (continuous)

Answer 13

Var(X)=∫(x−μ)^2 f(x)dx