Download Probability, Part 1 - Cascade Ridge Math Club

Name: _________________________________
Simple Probability
March 4, 2012
1. A bag contains 3 red marbles, 4 blue marbles, and 2 green marbles. If John picks a marble
from the bag without looking, what is the probability it will be red or blue? Write the
probability as a fraction.
2. What is the probability that a randomly chosen phone number ends in 4, 5, or 6? Express your
answer as a percentage.
3. There are three flavors of fruit chews in a bag: strawberry, orange and lemon. There are 4
strawberry chews. If you choose a fruit chew randomly from the bag, the probability of getting
orange is 3/7, and the probability of getting lemon is 2/7. How many fruit chews are in the bag?
4. In one of his choruses, Justin Bieber sings:
Baby, baby, baby, oh
Like baby, baby, baby, no
Like baby, baby, baby, oh
I thought you'd always be mine, mine
If you choose a word at random from these lyrics, what is the probability that the word would
be “baby”? Express your answer as a reduced fraction.
5. Chris Cross is 13 months old, and is at the prime age to learn to walk. He zigzags across the 12 by
15 foot room shown in the figure, eventually falling down. The ice cream cone he is carrying
spills either on the 9 by 12 foot rug or on the floor around the rug. What is the probability the
ice cream will land on the floor? Express your answer as a percentage.
6. In the board game Monopoly, you roll two dice to determine the number of spaces you move. If
you roll “doubles”, that is, the same number on each die, you get an extra turn. Assuming you
are rolling two fair six-sided dice, what is the probability of rolling doubles on any given turn?
Express your answer as a reduced fraction.
7. Bella, in her quest to get dressed for today’s math competition, needs to pick out two of the
same colored socks. She has ten blue socks, eight green socks, and six pink socks, and she
randomly selects socks from her drawer. In the unluckiest case, what is the minimum number
of socks she would have to pull out to guarantee that she has a pair of the same color?
8. The pages of a book are numbered consecutively from 1 through 177 inclusive. If a page is
chosen at random, what is the probability that the page number will contain the digit "1"?
Cascade Ridge PTSA Math Club
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Name: _________________________________
Simple Probability
March 4, 2012
BONUS PROBLEMS
9. If you roll two dice, what is the probability that the sum of the dice will be 8 or more? Express
your answer as a reduced fraction.
10. What is the probability that a randomly selected 2 digit number is divisible by 8? Answer as a
common fraction.
11. If you were to draw a single card from a deck of 52 cards, what is the probability of getting a
card with a prime number on it? Answer as a reduced fraction.
12. The Ratio of boys to girls at this math contest is 4:3. If each student has an equal chance of
winning, what are the odds that the winner will be a girl? Express your answer as a reduced
fraction.
Cascade Ridge PTSA Math Club
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Name: _________________________________
Simple Probability
March 4, 2012
SOLUTIONS:
1. 7/9
7 of the marbles are either red or blue, and there are a total of 9 marbles in the bag. So the
probability is 7/9.
2. 30%
Possible ending digits for a phone number are 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. The chance of ending
in 4, 5, or 6 is 3 out of the 10 possibilities, or 30%.
3. 14
There are only three flavors: orange, lemon, and strawberry. Since the probability of getting
orange is 3/7, and the probability of getting lemon is 2/7, then the remaining probability of
getting strawberry must be 2/7, since all three need to add up to 1 whole. So if the probability
of getting strawberry is 2/7, and there are 4 strawberry chews, then there must be 14 total
chews in the bag. 4/14 = 2/7.
4. 3/7
There are 21 words in the chorus and 9 of them are “baby”. Therefore, the chance of picking
“baby” at random is 9/21, which reduces to 3/7.
5. 40%
The total area of the room is 12 x 15, or 180 ft2. The area of the rug is 9 x 12, or 108 ft2. The
area of the room not covered by the rug is 180 - 108 = 72 ft2. Therefore, the chance that the ice
cream will land on the floor is 72/180, or 40%.
6. 1/6
Die 1
Possible combinations for the two dice are:
Die 2
1
2
3
4
1 1&1 1&2 1&3 1&4
2 2&1 2&2 2&3 2&4
3 3&1 3&2 3&3 3&4
4 4&1 4&2 4&3 4&4
5 5&1 5&2 5&3 5&4
6 6&1 6&2 6&3 6&4
5
1&5
2&5
3&5
4&5
5&5
6&5
6
1&6
2&6
3&6
4&6
5&6
6&6
Of the 36 possibilities, 6 are doubles. 6/36 reduces to 1/6.
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Simple Probability
March 4, 2012
7. 4
Since she has three different colors of socks, if she chooses 2 socks, they could be two different
colors. If she chooses 3 socks, they could also all be different colors. But if she chooses 4 socks,
at least two of them would have to be the same color.
8. 97/177
There are a total of 177 pages in the book. 97 of them contain the digit 1:
1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, 100,
101, 102, 103, ...., 175, 176, 177
So the probability is 97/177.
9. 5/12
Die 1
Possible combinations for the two dice are:
Die 2
1
2
3
4
1 1&1 1&2 1&3 1&4
2 2&1 2&2 2&3 2&4
3 3&1 3&2 3&3 3&4
4 4&1 4&2 4&3 4&4
5 5&1 5&2 5&3 5&4
6 6&1 6&2 6&3 6&4
5
1&5
2&5
3&5
4&5
5&5
6&5
6
1&6
2&6
3&6
4&6
5&6
6&6
Of the 36 possibilities, 15 add up to 8 or more. 15/36 reduces to 5/12.
10. 11/90
There are 90 two digit numbers. Looking at the multiples of 8 (16, 24, 32, 40, 48, 56, 64, 72, 80,
88 and 96), we find 11 two digit numbers that are divisible by 8. Therefore, the probability is
11/90.
11. 4/13
Cards with prime numbers include 2, 3, 5, and 7. Each deck contains 4 of each card, so there
would be 16 prime cards out of 52 total. 16/52 reduces to 4/13.
12. 3/7
A ratio of 4:3 means that for every 7 kids, 4 will be boys and 3 will be girls. The chance that the
winner will be a girl is 3/7.
Cascade Ridge PTSA Math Club
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