ALGEBRA 2/TRIG
Name:_________________________________ Date:_____________
12.5: Probability of Independent and Dependent Events
Probabilities of More than One Event: P(A and B) = P(A)  P(B)
 Independent Events:
 Events are not related
 ______________ replacement: whatever is picked is put back before second pick
o Denominator stays the ____________
 Dependent Events:
 Events are related
 ______________replacement: whatever is picked is NOT put back before second pick
o Denominator decreases by ______________ each time.
 How many fractions should I multiply?
 You should multiply the same number of fractions as the number of objects you are choosing
Examples: Order is Specified
1.) You are playing a game that involves spinning the money wheel shown.
During your turn, you get to spin the wheel twice. What is the probability
that you get more than $500 on your first spin and then go bankrupt on your
second spin?
2.) A game machine claims that 1 in every 15 people win. What is the probability that
you win three times in a row?
3.) A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles:
a) with replacement
b) without replacement
4.) A bag contains 3 red marbles, 7 white marbles, and 5 blue marbles. You draw 3 marbles, replacing each
one before drawing the next. What is the probability of drawing a red, then a blue, and then a white marble?
5.) A green die and a red die are tossed. What is the probability that a 4 shows on the green die, and a 5 shows
on the red die?
6.) You randomly select two cards from a standard 52-card deck. What is the probability that the first card is
not a face card and the second card is a face card with replacement? Without replacement?
7.) There are 6 pennies, 9 nickels, and 3 dimes in a box. Find the probability of…
a) P(2 nickels)—without replacement:
b) P(1 nickel and then a dime)—with replacement:
c) P(1 nickel and then 1 dime)—without replacement:
d) P(1 penny and then 2 nickels)—without replacement:
8.) From a standard deck of cards:
a) What is the probability of choosing a red and then a club with replacement?
b) What is P(a 3, then a 7, then a face card) without replacement?
c) What is P(a diamond, then a heart, then a black card) without replacement?
d) What is the probability of choosing a number card and then a face card with replacement?
9.) You and two friends go to a restaurant and order a sandwich. The menu has 10 types of sandwiches and
each of you is equally likely to order any type. What is the probability that each of you orders a different
type?
10.) Three friends are taking an English class that has a summer reading list. Each student is required to read
one book from the list, which contains 3 biographies, 10 classics, and 5 historical novels.
a) Find the probability that the first friend chooses a biography, the second friend chooses a classic, and the
third friend chooses a historical novel.
b) Find the probability that the three friends each choose a different classic.