Working with Probabilities

Question 1

Conditional Dependency

Probability of A given B
P ( A | B )

Answer 1

P(A and B) / P(B)

Question 2

Independent Events

Probability of A and B

Answer 2

P(A) * P(B)

Question 3

Independent Events

Probability of A or B

Answer 3

P(A) + P(B)

Question 4

Bayes’ Rules

Answer 4

Use to flip conditional probabilities

P( A | B ) = P( B | A ) * P(A) / P(B)

Question 5

Maximum Likelihood Estimation

Answer 5

Estimating probability from relative frequency

Probability of A given B
= count ( A & B ) / count (B)

Question 6

The Chain Rule

Answer 6

P (A1 & A2 & … & An-1 & An)
= P(An | An-1,…,A1) * P (An-1, …, A1)

P (A,B,C,D)
= P( D | C,B,A ) * P( C | B,A ) * P( B | A ) * P(A)

Question 7

The Markov Assumption

Answer 7

When we’re looking at the probability of An given A1 through An-1, we only need to look a few words back

You only need to look at the previous few words to estimate the probability of the current word

P (An | An-1, An-2)