Notes 13-3
Basic Probability
Warm-up
Page 864 #48
I.
A.
B.
C.
D.
Probability:
Measure the chances of something
happening.
Sample Space – set of possible
outcomes
Event – any subset of the sample
space
Success – when desired outcome is
received (p)
E.
F.
G.
H.
I.
Failure – when desired outcome
is NOT received (1-p)
P(certain) = 1
P(impossible) = 0
All probabilities are between
zero and one
Formula:
P( success ) 
success
number of outcomes in event
, P E  
success  failure
total outcomes in sample space
J.
Independent events –

2 things happen without affecting each
other.
 Two or more trials
 P
.  A  B  P A PB
K.
Mutually Exclusive Events–



Two possible results for a single trial
“Or” is used to describe the events.
.P  AorB   P  A  P  B 
L.
Expected Value (mean)



M.
Average value of the outcomes
Multiply each value by its probability and
add the results
In Calc, 1VARSTATS L1,L2
Probability Density Functions


Sum of area of probabilities is 1
Graph of probability distribution
II. Examples
A box contains 50 candies. Twenty are strawberry, 15 are
grape, 10 are lemon, and 5 are orange. One candy is
selected from the box and the flavor is observed.
1. Give the sample space for the experiment.
2. What is the probability that a strawberry or orange
candy will be drawn?
3. Is getting a lemon or getting an orange mutually
exclusive?
II. Examples
A box contains 50 candies. Twenty are strawberry, 15 are
grape, 10 are lemon, and 5 are orange. One candy is
selected from the box and the flavor is observed.
4. Create a probability distribution and probability
density function.
Flavor
Probability
Strawberry
Grape
Lemon
Orange
II. Examples
5. The table below shows the probability distribution of the
payoff on a $1 scatch-off lottery ticket. Find the
expected value. Interpret these results.
Payoff
$0
Probability 0.91176
$5
$10
$20
$50
$100
$1000
0.06
0.02
0.006
0.002
0.0002
0.00004
6) The probability of losing a certain game is 0.7. If
the game is played twice, what is the probability of:
a. Losing both times?
b. Winning both times?
c. Losing once and winning once?