12- 7 Theoretical and Experimental Probability
Quick Review
An event is an outcom e or group of outcom es. The
probability of an event, w hich indicates how likely it is to
occur, is w ritten P (event). W hen all possible o utcom es are
equally likely, th e th eo retical p ro b ab ility of an event is
u nf ,, number of favorable outcomes
given y (even ) number of possible outcomes 'Ex a m p l e
What is the theoretical probability that a randomly ch osen
date is a day beginning with a T?
There are 2 favorable outcom es, Tuesday an d Thursday.
There are 7 possible outcom es, th e 7 days of th e week.
,... , rr., number of favorable outcomes
P (d ay beginning with a T) = num berof possible outcomes
_ 2(^7) o
The probability of a day beginning w ith a T is y.
Ex e r c i se s
The spinner at the right is
divided into six equal sections.
Find the theoretical probability
o f landing on the given sections
o f the spinner.
- P(even)
- P(5)
- P(7)
38. P(odd)
40. P(not3)
42. P(morethan4) - Apples An apple farm er finds th a t he has to throw
out 15 b ad apples from th e 225 h e h as picked. W hat
is th e experim ental probability th a t th e next apple he
picks will be good?
12-8 Probability of Compound Events
Quick Review
You can use a form ula to find th e probability of a com pound
event involving two events A and B.
Mutually exclusive events: P(A or B) = P(A) + P(P)
Overlapping events:
P{A or B) = P{A) + P{B) - P{A and B)
In d e p en d en t events: P(A and B) = P(A) • P[B)
Dependent events: P(A th e n B) = P(A) • P{B after A)Ex a m p l e
You roll a num ber cube and flip a coin. What is the
probability that you roll a 5 and the coin com es up heads?
Rolling a 5 an d flipping h eads are in d ep en d e n t events.
P(5 and heads) = P(5) * P(heads) = | \ ^
The probability of rolling a 5 a n d flipping h ea d s isEx e r c i se s
You randomly pick two m arbles from a bag containing
3 yellow marbles and 4 red marbles. You pick the
second marble without replacing the first marble. Find
each probability.- P (re d th e n red) 45. P(yellow then red)
You roll a num ber cube twice. Find each probability. - P(6then3) 47. P (o d d th e n even)
Are the two events dependent or independent? Explain. - You pick one of 7 n am es from a h a t an d th e n pick a
second n am e w ithout replacing th e first one. - You spin a sp in n er w ith 5 equal sections an d pick a
m arble from a bag containing 2 green m arbles and
4 b lue m arbles.
790 Ch ap t er 12 Ch ap t er Rev i ew