Download Worksheet #2 Theoretical Probability

Probability
1. For a certain carnival game, you can win a prize if you throw two darts at the square board
pictured below and both darts hit the board. You win a poster for hitting an even number or a CD for
hitting the target on two of the same numbers; you win nothing for a single odd number. Each
numbered square is the same size.
1
2
3
2
1
3
a. For the target, list the following probabilities:
1) Hitting an even number throwing 1 dart ____________________
2) Hitting two of the same number throwing 2 darts____________________
3) Hitting an odd number throwing 1 dart____________________
4) Hitting a 5 throwing 1 dart
b. What is the total number of outcomes for throwing two darts? ________
4. Find the following probabilities relating to the dart board. For each problem, assume you hit the
board.
a. P (even number the first dart) =
b. P (first an even number, then an odd number) =
c. P (first an even, then an even) =
d. P (first a 2, then a 3) =
e. P (sum of 4) =
f. P (2,2) =
4. You roll two (6-sided) number cubes, a red one and a white one. Find each probability:
a. P(5,2)
b. P(5, odd #)
c. P(3,3)
d. P(even #, odd #)
e. P(4,4)
f. P((less than 5, 6)
5. You have 6 chips numbered 1 through 6 in a cup. You pull one out, then another out without
replacing the first one. Find each probability:
a. P(5, 2)
b. P(5, odd #)
c. P(3,3)
d. P(even #, odd #)
e. P(4,4)
f. P((less than 5, 6)
6. Find the probability of each event. Use a standard deck of 52 playing cards.
a) P (heart)
b) P (heart, heart) [without replacement]
c) P (heart, heart, heart) [w/ replacement]
d) P (heart, heart, heart, heart) [w/o replacement]
Candy Land Time!
Research the hit board game Candy Land.
Assuming there is the same number of each color of cards (ignore the special cards, the special cards
have been removed from the deck) in the deck, cards are replaced and reshuffled after every move.
There are 48 cards in the deck. What is the probability of pulling 2 purple cards in a row?
Why? Provide your justification in complete sentences. Diagrams are welcomed.
Life or Death
You have been captured by an evil warlord who decides to let you “decide” your fate. If you pick a
red marble you will be release and set free. If you select a blue marble you will be put to death.
You are given two jars, 50 red marbles, and 50 blue marbles. You need to place all the marbles into
the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it
will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of
that jar) you can arrange the marbles however you like, but each marble must be in a jar.
Marble Bag
You have a bag of white, gray, and black marbles (2 white, 4 gray, 1 black)
1. What is the probability of drawing a white marble then a black marble (no replacement)?
2. What is the probability of drawing 2 gray marbles (no replacement)?
3. What is the probability of drawing a white marble and a gray marble (no replacement)?
4. What is the probability of drawing 4 gray marbles (no replacement)?
5. What is the probability of drawing 4 white marbles (no replacement)?
6. What is the probability of flipping a coin 6 times and getting all heads?
7. If I have a 20 question multiple-choice test, each question has 4 possible answers (A, B, C, D),
how many ways is there to answer the test?
8. If I have a 20 question multiple-choice test, each question has 4 possible answers (A, B, C, D),
what is the probability of me randomly answering every question correctly?