Probability WITH ReplacementIndependent Events
The Aardvarks are playing the Baboons in a best of three games series. The probability of the Aardvarks winning any game is 4/5.
Find the probabilities. Write them as a fraction, a decimal, and a percent.
1.P(Aardvarks win in 2 games)_____2.P(Aardvarks win in 3 games)_____
In a big game, Fraser is fouled and awarded two free throws. The probability that Fraser will make a free throw is 4/5.
Find the probabilities. Write them as a fraction, a decimal, and a percent.
3.P(He scores 2 points)_____4.P(He will not score.)_____
A bag contains two red and four green marbles. Arabella draws one, replaces it, and draws a second.
Find the probabilities. Write them as a fraction, a decimal, and a percent.
6.P(Green, then Red)______7.P(Green, then Green)______
8.P(Red, then Red)______9.P(Red, then Green)______
10.Which outcome is most likely?______
Probability WITHOUT ReplacementDependent Events
A deck of cards consists of four Aces and three Kings. AAAAKKK
Three cards are drawn without replacement. Determine the following probabilities.
1.P(all aces) _____2.P(all Kings) _____3.P(2 Aces & 1 King)_____
Sorcha has 8 red and 4 green socks in a drawer. In the morning, it is dark in his room and she blindly
chooses one and then a second. Determine the probability that she chooses a matched pair.
4.P(red, then red)_____5.P(green, then green)_____
To improve her probability of choosing a matched pair, Sorcha buys two more pair of green socks.
What is her probability of choosing a pair now?
6.P(red, then red)_____7.P(green, then green)_____
A hat has seven disks in it numbered from 1 to 7. A disk is chosen, not replaced, and a second disk is chosen.
8.P(even, even)_____9.P(even, odd)_____
10.P(3, odd)_____11.P(3, 3)_____
Given a standard deck of 52 cards. Two cards are drawn in succession (one right after the other).
12.P(red, red)_____13.P(heart, heart)_____
14.P(Ace, Ace)_____15.P(9, 10)_____
Hanley draws three cards from a standard deck of 52 cards without replacement Find the probabilities.
16.P(black, black, black)_____17.P(diamond, diamond, black)_____
Probability for Mutually Exclusive Events
1.A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either
7 or 11?
2.A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either an even
number or a multiple of 3?
3.From a bag containing 5 white balls, 2 black balls, and 11 red balls, 1 ball is drawn. What is the
probability that it is either black or red?
4.What is the probability of drawing either a king, a queen, or a jack from a standard deck of 52 playing
cards?
5.What is the probability of rolling a die twice and having a 5 and then a 3 show or having a 2 and then a
4 show?
6.When tossing a coin, you have what probability of getting either a head or a tail?
7. A bag contains 12 blue, 3 red, and 4 white marbles. What is the probability of drawing
a. in 1 draw, either a red or a white marble?
b. in 1 draw, either a red, white, or blue marble?
c. in 2 draws, either a red marble followed by a blue marble or a red marble followed by a
red marble?
8. What is the probability of getting a total of at least 10 points in rolling two dice? (HINT: You
want either a total of 10, 11, or 12.)
Probability of Overlapping Events
P(A or B) = P(A) and P(B) – P(A and B)
Probability of Compound Events (Complex)
Two dice are rolled at the same time.
1.List the possible values on the dice 2.List the possible values on the dice if
if the sum must be equal to 3. How manythe sum must be equal to 4. How many
possible ways can you get a sum of 3?possible ways can you get a sum of 4?
3.List the possible values on the dice4.List the possible values on the dice if
if the sum must be equal to 13. How manythe sum must be greater than or equal to 7.
possible ways can you get a sum of 13?How many possible way can you get a
sum that is greater than or equal to 7?
5.List the possible values on the dice
if the sum must be less than or equal to 13.
How many possible way can you get a sum
that is less than or equal to 13?
Thinking about Probability….
Rolling one die:
1. P(1) = ______P(4) = ______P(1 and 4) = ______P(sum of 5) = _____
2.P(2) = ______P(6) = ______P(2 and 6) = ______P(sum of 8) = _____
3.P(5) = ______P(5) = ______P(5 and 5) = ______P(sum of 10) = _____
4.P(side) = ______P(side) = ______P(side and side) = ______P(sum) = _____
Rolling two dice:
5.P(side and side) = _____P(sum) = _____
The only thing that changes is the number of ways that you can get the sum.
6.In how many ways can you get a sum of 5?7.In how many ways can you get a sum of 8?
1and4 or 2and3 or 3and2 or 4and1
1way + 1way + 1way + 1way
4 ways
Two dice are rolled at the same time. Find the following probabilities.
8.P(sum = 3)______9.P(sum = 4)_____
10.P(sum = 13)_____11.P(sum > 7)_____
12.P(sum < 13)_____13.P(sum = 6)_____
Probability of Compound Events
(Is a Spinner the same as dice?)
6. If you spin the spinner twice, what is the probability that you will have a sum of $200?
7. If you spin the spinner twice, what is the probability that you will have a sum of at most $400?
8. If you spin the spinner twice, what is the probability that you will have a sum of at least $1500?
9. Given that you landed on $100 on the first spin, what is the probability that the sum of your two spins
will be $200?
10. Given that you landed on $800 on the first spin, what is the probability that the sum of your two spins
will be at least $1500?