Probability & Statistics - Grade 5

Transcription

1 2006 Washington State Math Championship nless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Probability & Statistics - Grade 5 1. A single ten-sided die is rolled once. What is the probability that the result is NOT prime? Answer in a reduced fraction. 2. A single card is drawn from a deck of cards. What is the probability it is NOT a face card? Answer in a reduced fraction. 3. According to the quote by mathematician Nikolai Lobachevsky, There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. If you randomly select a letter from this quote, what is the probability that the letter is a vowel? (Note: Y is not considered a vowel.) Answer as a reduced fraction. 4. Aaron has been keeping track of the length of slugs he finds along the trail. He has found 9 so far with an average length of 12.5cm. Then he found a monster slug large enough to raise the average to 13.75cm. How many times longer was this monster slug than the original average (12.75)? Answer as a decimal. 5. The average of 8 whole numbers is 8. If 7 of these numbers are 1 then the eighth must be what number? 6. When 5 fair coins are flipped, what is the probability that exactly two of them show tails? Answer in a reduced fraction. 7. Two dice are rolled and the smaller number is subtracted from the larger number. What is the probability that the difference of the two dice is a prime number? Answer in a reduced fraction. 8. Given the diagram: S P P P E E E E R R R R R How many different paths through the diagram spell SPER by starting at the top and selecting letters as you move down.

2 9. A particle moves randomly along a number line in single unit jumps starting at zero, and is equally likely to move left or right for a move. What is the probability that it is back at zero after four moves? Answer as a reduced fraction. 10. Five boys and four girls go to a movie and sit in the same row. How many ways can they arrange themselves if no two girls or boys sit together?

3 2006 Washington State Math Championship nless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Probability & Statistics - Grade 6 1. Aaron has been keeping track of the length of slugs he finds along the trail. He has found 9 so far with an average length of 12.5cm. Then he found a monster slug large enough to raise the average to 13.75cm. How many times longer was this monster slug than the original average (12.75)? Answer as a decimal. 2. The average of 8 whole numbers is 8. If 7 of these numbers are 1 then the eighth must be what number? 3. When 5 fair coins are flipped, what is the probability that exactly two of them show tails? Answer in a reduced fraction. 4. Two dice are rolled and the smaller number is subtracted from the larger number. What is the probability that the difference of the two dice is a prime number? Answer in a reduced fraction. 5. Given the diagram: S P P P E E E E R R R R R How many different paths through the diagram spell SPER by starting at the top and selecting letters as you move down. 6. A particle moves randomly along a number line in single unit jumps starting at zero, and is equally likely to move left or right for a move. What is the probability that it is back at zero after four moves? Answer as a reduced fraction. 7. Five boys and four girls go to a movie and sit in the same row. How many ways can they arrange themselves if no two girls or boys sit together?

4 8. A total of 100 beads (50 Black and 50 White) are placed in two identical boxes so that one box contains only one bead (a black one), and the other box has the other 99 beads. What is the probability of choosing a black bead from a randomly chosen box? Answer to the nearest percent. 9. Egore has a large number of relatives that he classifies according to the chart. What is the probability that random relative showing up that is Good Aunt OR Not gly? Answer as a reduced fraction. Aunts ncles Good 6 7 Bad 12 8 gly Students at a math contest were asked to try three new flavors of ice cream from the local ice cream parlor: Huckleberry, Chokecherry and Apple Dumpling. Eight people sampled all three. Forty-five had huckleberry, 56 had chokecherry and 63 had apple dumpling. Eighteen sampled both huckleberry and chokecherry, 26 tasted apple dumpling and chokecherry, and 20 had huckleberry and apple dumpling. How many people had only apple dumpling?

5 2006 Washington State Math Championship nless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Probability & Statistics - Grade 7 1. Two dice are rolled and the smaller number is subtracted from the larger number. What is the probability that the difference of the two dice is a prime number? Answer in a reduced fraction. 2. Given the diagram: S P P P E E E E R R R R R How many different paths through the diagram spell SPER by starting at the top and selecting letters as you move down. 3. A particle moves randomly along a number line in single unit jumps starting at zero, and is equally likely to move left or right for a move. What is the probability that it is back at zero after four moves? Answer as a reduced fraction. 4. Five boys and four girls go to a movie and sit in the same row. How many ways can they arrange themselves if no two girls or boys sit together? 5. A total of 100 beads (50 Black and 50 White) are placed in two identical boxes so that one box contains only one bead (a black one), and the other box has the other 99 beads. What is the probability of choosing a black bead from a randomly chosen box? Answer to the nearest percent. 6. Egore has a large number of relatives that he classifies according to the chart. What is the probability that random relative showing up that is Good Aunt OR Not gly? Answer as a reduced fraction. Aunts ncles Good 6 7 Bad 12 8 gly 3 11

6 7. Students at a math contest were asked to try three new flavors of ice cream from the local ice cream parlor: Huckleberry, Chokecherry and Apple Dumpling. Eight people sampled all three. Forty-five had huckleberry, 56 had chokecherry and 63 had apple dumpling. Eighteen sampled both huckleberry and chokecherry, 26 tasted apple dumpling and chokecherry, and 20 had huckleberry and apple dumpling. How many people had only apple dumpling? 8. Two darts are thrown at the square dart board where the sides of square B are twice as long as square A. What is the probability that both darts land on square A? Answer as a reduced fraction. A B 9. You are given 1001 increasing sequential integers starting at What is the median of sub-list from the 305 th term to the 508 th term? 10. The parking lot at Gypsum Bank has three spaces labeled Vice-President. However, there are seven vice-presidents. How many ways can the vicepresidents occupy these spaces?

7 2006 Washington State Math Championship nless a particular problem directs otherwise, give an exact answer or one rounded to the nearest thousandth. Probability & Statistics - Grade 8 1. Five boys and four girls go to a movie and sit in the same row. How many ways can they arrange themselves if no two girls or boys sit together? 2. A total of 100 beads (50 Black and 50 White) are placed in two identical boxes so that one box contains only one bead (a black one), and the other box has the other 99 beads. What is the probability of choosing a black bead from a randomly chosen box? Answer to the nearest percent. 3. Egore has a large number of relatives that he classifies according to the chart. What is the probability that random relative showing up that is Good Aunt OR Not gly? Answer as a reduced fraction. Aunts ncles Good 6 7 Bad 12 8 gly Students at a math contest were asked to try three new flavors of ice cream from the local ice cream parlor: Huckleberry, Chokecherry and Apple Dumpling. Eight people sampled all three. Forty-five had huckleberry, 56 had chokecherry and 63 had apple dumpling. Eighteen sampled both huckleberry and chokecherry, 26 tasted apple dumpling and chokecherry, and 20 had huckleberry and apple dumpling. How many people had only apple dumpling? 5. Two darts are thrown at the square dart board where the sides of square B are twice as long as square A. What is the probability that both darts land on square A? Answer as a reduced fraction. A B 6. You are given 1001 increasing sequential integers starting at What is the median of sub-list from the 305 th term to the 508 th term? 7. The parking lot at Gypsum Bank has three spaces labeled Vice-President. However, there are seven vice-presidents. How many ways can the vicepresidents occupy these spaces?

8 8. A particle moves randomly on a Cartesian-plane in one-unit jumps starting at the origin, and is equally likely to move left, right, up or down for it s one-unit move. No diagonal moves are possible. What is the probability that it is back at zero after four moves? Answer as a reduced fraction. y x 9. What is the probability of throwing two darts at the odd shaped dartboard and at least one hitting the shaded region? Express your answer as a percent rounded to the nearest whole percent The varsity math team, 4 boys and 8 girls, travels to an out-of-town contest to Blaine. Their coach, Miss Einstein will take 7 of them in her Hydrogen-Hybrid- Humvee (this story takes place in the future). If they get in to the cars at random, what is the probability that Miss Einstein s car has 2 boys and 5 girls? Give your answer in a reduced fraction.