Probability

Question 1

what’s the complement rule?

Answer 1

P(A) = 1 - P(not A)

P(not A) = 1 - P(A)

Question 2

what’s the probability of both A and B occurring?

Answer 2

trick question!

If A and B are not independent:
P(A and B) = P(A|B)P(B) = P(B|A)P(A)

and if they are independent:
P(A and B) = P(A)P(B)

Question 3

what’s the probability of A or B occurring?

Answer 3

P(A or B) = P(A) + P(B) - P(A and B)

note that P(A and B) depends on whether A and B are independent

Question 4

what’s the probability of A or B or both occurring?

Answer 4

if A and B are not independent:
P(A or B or (A and B)) = P(A) + P(B) + P(A|B)P(A) = P(A) + P(B) + P(B|A)P(B)

If A and B are independent:
P(A or B or (A and B)) = P(A) + P(B) + P(A)P(B)

Question 5

If A and B are mutually exclusive, then…

Answer 5

P(A and B) = 0

Question 6

If we have n elements, how many ways can we arrange them?

Answer 6

n!

Question 7

how many ways can we choose k elements from a set of n?

Answer 7

n! / (n-k)!

Question 8

the p-value is the probability of obtaining the data at least as extreme as observed if the null hypothesis is ______

Answer 8

true

Question 9

what’s the null hypothesis in linear regression?

Answer 9

that the feature has no relationship with the target (that its coefficient is 0)

Question 10

expand P(A|B)

Answer 10

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

Question 11

generally, or means ___ in probability

Answer 11

addition

Question 12

generally, and means ___ in probability

Answer 12

multiplication