2001 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. Dr. Don Pickett is a pediatric dermatologist. The ages of his patients for the last month are given in the table below. Based on these results, what is the probability that his next patient will be less that 8 years old?

Patient Age Group Number of Patients

0-3 83
4-7 37
8-11 22
12-15 96
16-19 19

2. A player’s batting average is calculated by dividing his number of hits by his number of at-bats. At the end of April, Edgar’s batting average was .361. Then he got 25 hits in his next 62 at-bats. If his total number of at-bats was then 145, what was his batting average?

3. Ty Score is a 63% passer. What is the probability that he completes his next 5 passes?

4. Two machines are each capable of generating random digits [0,9]. What is the probability that the sum of the digits generated by each machine is a prime number?

5. Jose Canusea has 3 flags, one red, one white, and one blue. He can fly these flags on his flag pole in any order three at a time, two at a time, one at a time, or none at a time. How many different messages can he send with this three flag system?

6. The probability that a needle of length 1 inch will touch one of the parallel lines spaced 1 inch apart when it is dropped randomly is . What is the probability that a 1-inch needle will not touch any of the grid lines in a 1-inch perpendicular grid?



7. If the radii of the concentric circles are 1 cm, 2 cm, 3 cm, 4 cm, and 5 cm, what is the probability that a point selected at random in the design is in the shaded area?



8. A player’s batting average can be thought of as the probability that he will get a hit, if we disregard walks, errors, and sacrifices that do not affect batting averages. If a pitcher is to face 3 batters with averages of .267, .298, and .345, what is the probability that he will get all three players out?

9. Mr. Ree had 25 students each ask 20 people whether they liked the Road Runner or the Coyote. Of the 500 different people asked, 320 liked the Road Runner. Maria was absent on the day of the survey so she needed to survey 20 more people. Based on the results of the the survey so far, arrange the following from most likely to least likely for the number of people Maria will survey who will pick the Road Runner: 8, 10, 13, 14.

10. In the addition cryptogram below each letter is to be replaced by a different digit. How many different ways can this be done?