Chapter 3 terms

Question 1

probability measure

Answer 1

P on a sample space maps subsets (boundaries)

Question 2

discrete sample space

Answer 2

any finite set/set that can be listed as {w1, w2, w3,…}

Question 3

P(A^c)

Answer 3

1-P(A) = everything but A

Question 4

Partition theorem

Answer 4

If B1, B2, B3,…. form a partition of sample space e.g. A1, A2, A3 all add to Event A.

P(A) = P((AnB) U (AnB^c))

Question 5

If ACB then P(A) < P(B)

Answer 5

P(A) fits into P(B)
P(B) =P(AnB) + P(A^cnB)
= P(A) + P(A^cnB) since ACB
= P(A) < P(B) since P(A^cnB) > 0

Question 6

P(AUB)

Answer 6

=P(A) + P(B) - P(AnB) (take out the intersection as included twice)

Proof: P(AuB) = P(AU(A^cnB)) chapter 2
= P(A) + P(A^c n B) definiton
= P(A) + P(B) - P(AnB) partition

Question 7

Events and probabilities

Answer 7

Probabilities use + and x

Events use n and u

Question 8

randomly chosen

Answer 8

equally likely chance of being selected

Question 9

equally likely outcomes

Answer 9

i) sample space = {w1, w2, w3,…}
ii) P({w1}) = P({w2}) = … = P({wk}) = 1/k
iii) event A C sample space contains r possible outcomes

then P(A) = number of outcomes in A/number of outcomes in sample space = r/k

Question 10

permutations

Answer 10

when order matters
#permutations = n^P_r = n(n-1)(n-2) ... (n-r+1) = n!/(n-r)!

n choices for first object, (n-1) choices for second

Question 11

combinations

Answer 11

when order does not matter
#combinations = n^C_r = (n/r) = n^P_r/r! = n!/(n-r)!r!

because n^P_r counts all r! possible orderings of the r objects