2003 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded to the
nearest thousandth.
Probability - Grade 5
1.
What is the probability that a randomly chosen phone number ends in 4 , 5 , or 6 ?
2.
What is the probability that a randomly selected 2 digit number is divisible by 8 ? Answer as
a common fraction.
3.
There are 14 yellow marbles, 5 red marbles, and 21 blue marbles in a sock. If one marble is
drawn out, what is the probability that is is not blue?
4.
Find the mean of the weights of salmon caught in the salmon derby. The weights in pounds
1
1
1
are: 9, 6, 24, 15, 15, 10 , 18, 21, 18 , 7 , 12, 4
2
2
2
5.
Find the median of the weights of salmon caught in the salmon derby. The weights in pounds
1
1
1
are: 9, 6, 24, 15, 15, 10 , 18, 21, 18 , 7 , 12, 4
2
2
2
The 5 digit number, 37 x 33 , is divisible by 3 where x represents the middle digit. What is
the probability that x = 5 ?
6.
7.
What is the probability that a randomly selected 2 digit number is prime? Answer as a
reduced fraction.
8.
A drawer contains 18 socks, some black and some white. Two socks are randomly drawn
from the drawer. The probability that both socks are black is 26/51 . How many socks in
the drawer are white?
9.
At gasoline pumps the number of gallons of gasoline delivered is measured to the nearest
thousandth of a gallon. The pump shuts off automatically when the gas tank is full. For
example, when Phil Uppe got gas last week, the pump shut off at 12.633 gallons. At a
random fill-up the last 3 decimal places can be thought of as a random number generator.
What is the difference in the probability that the last 3 decimal places are 724 and that they
are 000?
10.
Foot Draggers sold the following sizes of basketball shoes last month. Based on this data,
what is the probability that the next customer who buys basketball shoes will buy a half-size?
Answer to the nearest thousandth.
Size
7
7
Number sold
of each size
2
5
1
2
8
9
1
2
15
8
9
19
1
2
16
9
10
10
7
6
1
2
11
3
2003 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded to the
nearest thousandth.
Probability - Grade 6
1.
Find the mean of the weights of salmon caught in the salmon derby. The weights in pounds
1
1
1
are: 9, 6, 24, 15, 15, 10 , 18, 21, 18 , 7 , 12, 4
2
2
2
2.
Find the median of the weights of salmon caught in the salmon derby. The weights in pounds
1
1
1
are: 9, 6, 24, 15, 15, 10 , 18, 21, 18 , 7 , 12, 4
2
2
2
The 5 digit number, 37 x 33 , is divisible by 3 where x represents the middle digit. What is
the probability that x = 5 ?
3.
4.
What is the probability that a randomly selected 2 digit number is prime? Answer as a
reduced fraction.
5.
A drawer contains 18 socks, some black and some white. Two socks are randomly drawn
from the drawer. The probability that both socks are black is 26/51 . How many socks in
the drawer are white?
6.
At gasoline pumps the number of gallons of gasoline delivered is measured to the nearest
thousandth of a gallon. The pump shuts off automatically when the gas tank is full. For
example, when Phil Uppe got gas last week, the pump shut off at 12.633 gallons. At a
random fill-up the last 3 decimal places can be thought of as a random number generator.
What is the difference in the probability that the last 3 decimal places are 724 and that they
are 000?
7.
Foot Draggers sold the following sizes of basketball shoes last month. Based on this data,
what is the probability that the next customer who buys basketball shoes will buy a half-size?
Answer to the nearest thousandth.
Size
7
7
Number sold
of each size
2
5
1
2
8
9
1
2
15
8
9
19
1
2
16
9
10
10
7
6
1
2
11
3
8.
Two dice are rolled. What is the probability that the absolute value of their difference is
greater than 2?
9.
Two dice are rolled. What is the probability of getting a six on either die or a sum of 6 on
both dice?
10.
A security gate at the marina can be opened with four-digit access codes, for example, 0384.
Each person needing access through the gate is given a own code by the marina. Richard tries
some random four-digit numbers and discovers that 1234 opens the gate. However, the
marina changes the security system from a 5-button system to a 10-button system (pictured
below) so that all the members 4-digit codes still work. Richard discovers that 1234 does not
work. What is the minimum number of 4-digit codes that Richard needs to try to be sure of
opening the security gate?
1-2
1
2
3-4
3
4
5-6
5
6
7-8
7
8
9-0
9
0
5-button
system
10-button
system
2003 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded to the
nearest thousandth.
Probability - Grade 7
1.
What is the probability that a randomly selected 2 digit number is prime? Answer as a
reduced fraction.
2.
A drawer contains 18 socks, some black and some white. Two socks are randomly drawn
from the drawer. The probability that both socks are black is 26/51 . How many socks in
the drawer are white?
3.
At gasoline pumps the number of gallons of gasoline delivered is measured to the nearest
thousandth of a gallon. The pump shuts off automatically when the gas tank is full. For
example, when Phil Uppe got gas last week, the pump shut off at 12.633 gallons. At a
random fill-up the last 3 decimal places can be thought of as a random number generator.
What is the difference in the probability that the last 3 decimal places are 724 and that they
are 000?
4.
Foot Draggers sold the following sizes of basketball shoes last month. Based on this data,
what is the probability that the next customer who buys basketball shoes will buy a half-size?
Answer to the nearest thousandth.
Size
7
7
Number sold
of each size
2
5
1
2
8
9
1
2
15
8
9
19
1
2
16
9
10
10
7
6
1
2
11
3
5.
Two dice are rolled. What is the probability that the absolute value of their difference is
greater than 2?
6.
Two dice are rolled. What is the probability of getting a six on either die or a sum of 6 on
both dice?
7.
A security gate at the marina can be opened with four-digit access codes, for example, 0384.
Each person needing access through the gate is given a own code by the marina. Richard tries
some random four-digit numbers and discovers that 1234 opens the gate. However, the
marina changes the security system from a 5-button system to a 10-button system (pictured
below) so that all the members 4-digit codes still work. Richard discovers that 1234 does not
work. What is the minimum number of 4-digit codes that Richard needs to try to be sure of
opening the security gate?
1-2
1
2
3-4
3
4
5-6
5
6
7-8
7
8
9-0
9
0
5-button
system
10-button
system
8.
In the previous problem the marina’s change from a 5-button to a 10-button system makes
possible how many more 4-digit codes?
9.
The outside figure is a square. Other squares are formed by connecting the midpoints of the
sides of the squares. If a point in the figure is selected at random, what is the probability that
it is shaded? Answer as a reduced fraction.
10.
Ichiro’s on-base average (the probability of getting on base at any at-bat) is 0.418 . Mark’s
is 0.384 , and John’s is 0.408 . If these three come to bat in the same inning, what is the
probability, to the nearest thousandth, that none get on base?
2003 Washington State Math Championship
Unless a particular problem directs otherwise, give an exact answer or one rounded to the
nearest thousandth.
Probability - Grade 8
1.
Foot Draggers sold the following sizes of basketball shoes last month. Based on this data,
what is the probability that the next customer who buys basketball shoes will buy a half-size?
Answer to the nearest thousandth.
Size
7
7
Number sold
of each size
2
5
1
2
1
2
15
8
8
9
9
19
1
2
16
9
10
10
7
6
1
2
11
3
2.
Two dice are rolled. What is the probability that the absolute value of their difference is
greater than 2?
3.
Two dice are rolled. What is the probability of getting a six on either die or a sum of 6 on
both dice?
4.
A security gate at the marina can be opened with four-digit access codes, for example, 0384.
Each person needing access through the gate is given a own code by the marina. Richard tries
some random four-digit numbers and discovers that 1234 opens the gate. However, the
marina changes the security system from a 5-button system to a 10-button system (pictured
below) so that all the members 4-digit codes still work. Richard discovers that 1234 does not
work. What is the minimum number of 4-digit codes that Richard needs to try to be sure of
opening the security gate?
1-2
1
2
3-4
3
4
5-6
5
6
7-8
7
8
9-0
9
0
5-button
system
5.
10-button
system
In the previous problem the marina’s change from a 5-button to a 10-button system makes
possible how many more 4-digit codes?
6.
The outside figure is a square. Other squares are formed by connecting the midpoints of the
sides of the squares. If a point in the figure is selected at random, what is the probability that
it is shaded? Answer as a reduced fraction.
7.
Ichiro’s on-base average (the probability of getting on base at any at-bat) is 0.418 . Mark’s
is 0.384 , and John’s is 0.408 . If these three come to bat in the same inning, what is the
probability, to the nearest thousandth, that none get on base?
8.
The probability that the earth will be hit by a meteorite greater than 1000 feet in diameter in
1
any one year is
. After how many years will the probability of the earth being hit by
1000
1
such a meteorite be greater than ?
2
9.
Two 12-sided (dodecahedral) dice are rolled. The number 1 through 12 are on the faces of
each die. What is the probability that the sum of the top faces of each die is divisible by 5?
Answer as a reduced fraction.
10.
A penny, nickel, dime, and quarter are flipped. What is the probability of getting at least 2
heads?