Download Math 112 Probability Worksheet

MacMillan/Manuel
1.
a)
b)
c)
d)
e)
Math 112A Probability Worksheet
Which of the following events are independent? Dependent?
Name:_______________________
Throwing a 4 with one die and a 6 with another.
Picking a 7 from a deck of cards, keeping it, and picking a jack.
Flipping a tail with a coin and rolling a 4 with a die.
Drawing a spade and drawing a heart from the same deck without replacing the first card.
Picking two black marbles from a bag of black and white marbles after replacing the first one.
2.
Two letters are chosen, without replacement, at random from the English alphabet. If y is considered to be a consonant, find the
probability that
a) both are vowels, b) both are consonants.
3.
A bag contains 4 white, 3 blue, and 6 red marbles. A marble is drawn from the bag, replaced, and another marble is drawn. Find
the probability that
a) both marbles are red
b) both marbles are blue
c) the first marble is red and the second is blue
d) one marble is red and the other is blue
e) neither is red
f) do a-e again and do not replace the marble
4.
Using a pair of dice, what is the probability of throwing a sum of nine twice in a row?
5. A box has 3 hockey and 6 football cards.
a) What is the probability of selecting a hockey card, keeping it out, and then selecting another hockey card?
b) What is the probability of selecting a hockey card, keeping it out, and then selecting a football card?
6.
A player rolls a pair of dice and then picks a card from a deck of cards. What is the probability of throwing a 10 and picking a
club?
7. A card is chosen from a deck of 52. Find…
a) P(a 4 or a diamond)
b) P(a face card or a club)
c) P(a black card or a card with a number)
8. Olga places 10 squares, 10 triangles, and 10 rectangles in a hat. On each is placed on of the numbers 0,1,2,…,9. One shape is
randomly selected from the hat, calculate each of the following.
a) P(square or a shape with an 8)
b) P(triangle or a shape with a 6)
c) P(rectangle or a shape with a 4)
d) P(rectangle or a shape with an even number)
e) P(square or a shape with an odd number) f) P(any shape or any shape with a number on it)
9. Jeff and George are skateboarders. Jeff successfully completes a certain stunt 1 out of every 5 attempts while George completes
the same stunt 1 out of every 4 attempts. Show how an area model could be used to determine the probability of Jeff or George
successfully completing the stunt on the first attempt. What is the probability?
10. a) Express 31x30x29x28x12x11x10 as a ratio of factorials
b) Evaluate 8!
c) Evaluate 4!3!
5!
Answers: (Place final answers in simplified form here – show your work on looseleaf)
1. a)__Independent__b)_ Dependent__ c)__Independent__ d) __Dependent_ e) __Independent__
2. a) __2/65__ b) __42/65__
3. With Replacement:
a) __36/169__ b) __9/169__ c) __18/169__ d) __18/169__ e) __49/169__
Without Replacement: a) __5/26____ b) __1/26___ c) __3/26____ d) __3/26____ f) __7/26____
5. a) ___1/12___ b) ___1/4___
6. ___1/48_____
4. __1/81__
7. a) _____4/13____ b) ____11/26_____ c) ____11/13___
8. a) ____2/5____ b) ____2/5___ c) _____2/5___ d) ___2/3___ e) ___2/3__ f) ____1____
9. ___2/5____
Area Model diagram
on looseleaf
10. a)
31! 12!
27! 9!
b) ____40 320_____
c) _____6/5____