Algebra II
Notes 3.1 Probability of Simple Events
The Probability of an event is the ratio of the number of favorable outcomes to the total number of
possible outcomes.
Probability =
number of ways an event can happen
total number of outcomes possible
The probability an event can happen must be between 0 and 1 (0 < P < 1).
If P(A) = 0, then event “A” cannot happen.
If P(A) = 1, then event “A” will occur for certain.
EX: A standard 6-sided die is rolled once. Find each probability.
a.) Find P(2). (This means the probability of rolling a 2.)
c.) Find P(number greater than 4).
b.) Find P(odd number).
d.) Find P(number less than 7).
e.) Find P(number greater than 7).
Odds – calculated and expressed as ratios. (Odds can be larger than 1 since it is a ratio)
Odds of Winning =
Odds of Losing =
number of winning outcomes
number of losing outcomes
number of losing outcomes
number of winning outcomes
EX: A ball is selected from a box that contains 5 red, 4 white, and 6 green balls. Find the odds
of drawing:
a.) one red ball.
b.) one green ball.
c.) not selecting a white ball.
d.) selecting a black ball.
You can also work backwards if given ODDS, you can find Probability.
Ex: Find the probability of success if the ODDS of success are 5:9.
5 = # of success
P(success) =
9 = # of losses.
number of successes
=
number of total outcomes
Notes 3.2 Probability of Compound Events
Independent Event – the outcome of an event has no affect on the outcome of another event.
Probability of Independent Events = P( A) ⋅ P( B)
Dependent Event – the outcome of an event is affected by the outcome of a previous event.
Probability of Dependent Events = P ( A) ⋅ P( B after A occurs)
Ex: A die is rolled twice. Find each probability.
a.) P(two odd numbers are rolled) = P(odd on first roll) · P(odd on second roll)
b.) A jar contains 3 red gumballs, 5 green gumballs, and 6 orange gumballs. Find the
probability that two green gumballs are chosen if no gumballs are replaced.
Probability of Event A or Event B Occurring
P(A or B) = P(A) + P(B)
← mutually exclusive events (no overlap in outcomes)
EX: Find the probability of selecting a black card or a heart from a deck of 52 cards.
P(A or B) = P(A) + P(B) – P(A and B) ← inclusive events (events that have overlap in
outcomes.)
EX: Find the probability of selecting a black card or a King from a deck of 52 cards.