Finite Math
section 7.2
Probabilities of Equally likely events
n(A)
For equally likely events, P(A) = n(S)
where n(A) = # of elements in A and n(S) = # of elements in Sample space.
Ex1,
1 die is rolled once.
(a) List the sample space and probability distribution.
Find the probability such that
(b) the roll is 4 or 5.
(c) the roll is even
Ex2,
1 small die and 1 large die are rolled. (2 dice are rolled).
(a) List sample space. What is the probability of each simple outcome?
Find the probability such that
(b) Sum of the rolls is 9.
(c) both rolls are even
(d) At least one die is 5
(e) At lease one die is 5 or 6
(f) At least one die is even
Ex3,
1 red die, 1 blue die, and 1 white die are rolled. Find the probability such that
(a) Sum of the rolls is 9.
(b) all same rolls
(c) At least one die is 5
(d) At lease one die is 5 or 6
(e) At least one die is even
Ex4,
There are 4 women and 3 men. The 3 men are Pedro, Brian, and Mike.
If a committee of 2 people is randomly selected, find the probablity that the committee consists of
(a) 2 women.
(b) 2 men.
(c) 1 women and 1 man.
(d) at least one man. ( P(at least 1 man) = P(S)  P(no man) = P(S)  P(all women)
(e) Find the probability that Pedro is selected.
(f) Find the probability that Pedro is NOT selected.
(g) Find the probability that Pedro is selected, but Mike is not selected.
(h) Find the probability that Mike and Brian are selected.
Ex5,
There are 4 women and 3 men. If a committee of 3 people is randomly selected,
find the probablity that the committee consists of
(a) 3 women.
(b) 3 men.
(c) 2 women and 1 man.
(d) 1 women and 2 men.
(e) at least one man.
(f) at least 2 women.