Questions Counting 1 A number is randomly chosen

Questions : Counting

1. A number is randomly chosen from a list of 10 consecutive positive integers. What is the probability that the number is greater than the mean? (A) 3/10 (B) 2/5 (C) 1/2 (D) 7/10 (E) 4/5

Ans. (C)

2. A restaurant menu has several options for tacos, There are 3 types of shells, 4 types of meat, 3 types of cheese, and 5 types of salsa. How many distinct tacos can be ordered assuming that any order contains exactly one of each of the above choices? 180 Given; shells 3 types meat 4 types cheese 3 types salsa 5 types Thus; distinct tacos can be ordered is 3 x 4 x 3 x 5 = 180

3. A certain company places a symbol code on each of their products. The first two symbols are one of the letters A-E and the last four symbols are digits. If repeats are allowed on both letters and numbers, how many such codes are possible?

The first two symbols the last four symbols are digits 1 2 3 4 5 6 (A-E) (0 -9) 5 5 10 10 Thus; 5 x 10 x 10 = 250, 000

4. An integer is randomly chosen from 2 to 20 inclusive. What is the probability that the number in prime? 8 19 Integer from 2 to 20 inclusive is 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 prime number from 2 to 20 inclusive is 2, 3, 5, 7, 11, 13, 17, 19 Thus; the probability that the number in prime from 2 to 20 inclusive is 8/19

5. An Italian restaurant boasts 320 distinct pasta dishes. Each dish contains exactly one pasta, one meat, and one sauce. If there are 8 pastas and 4 meats available, how many sauces are there to choose from? 10 Given; x = sauce From; 320 distinct pasta dishes, 8 pastas and 4 meats Thus; (8)(4)(x) = 320 32 x = 320 x = 10

6. Quantity A Quantity B The number of 4 -digit positive integers where all 4 digits are less than 5 625 Given; A, B, C, D is 4 digits are less than 5 The numbers can be possible ; A (4, 3, 2, 1) = 4 B (4, 3, 2, 1, 0) = 5 C (4, 3, 2, 1, 0) = 5 E (4, 3, 2, 1, 0) = 5 Thus; 4 x 5 x 5 = 500 Ans. B

7. The probability of rain is 1/6 for any given day next week. What is the chance it rains on both Monday and Tuesday? (A) 1/36 (B) 1/12 (C) 1/6 (D) 1/3 (E) 2/3 Ans. (A)

8. A bag contains 3 red, 2 blue, and 7 white marbles. If a marble is randomly chosen from the bag, what is the probability that it is NOT blue? 5 6

9. A state issues automobile license plates using two letters selected from a 26 -letter alphabet, as well as four numerals selected from the digits 0 through 9, inclusive. Repeats are permitted For example; one license plate combination could be GF 3352. Quantity A The number of possible unique license plate combinations Quantity B 6, 000

letter numerals 1 2 1 (A-Z) (0 -9) 26 26 10 2 3 4 (0 -9) 10 10 10 Thus; 26 x 10 x 10 = 6, 084, 000 Ans. (A)

10. A bag contains black chips numbered 1 -6 respectively and 6 white chips numbered 1 -6 respectively. If Pavel reaches into the bag of 12 chips and removes 2 chips, one after the other, without replacing them, what is the probability that he will pick black chip #3 and then white chip #3?

11. A bag contains 6 red chips numbered 1 -6 respectively and 6 blue chips numbered 1 -6 respectively. If 2 chips are to be picked sequentially from the bag of 12 chips without replacement, what is the probability of picking a red chip and then a blue chip with the same number? 1 22

Ans. (A)

13. A coin with heads on one side and tails on the other has a 1/2 probability of landing on heads, lf the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be heads? Outcomes are distinct if they do not contain exactly the same results in exactly the same order. 16

14. How many integers between 2, 000 and 3, 999 have a ones digit that is a prime number?

2000 -3999 ; ones digit of prime number is 2, 3, 5, 7 2002 2003 2005 2007 2012 2013 2015 2017 2022 2023 2025 2027. . 3982 3983 3985 3987 3992 3993 3995 3997 4 Thus; 4 x 200 = 800 ; 2000 -2010 ; 2011 -2020 ; 2021 -2030 ; 3980 -3990 ; 3991 -3999 200

15. Bob has a 24 -sided die with an integer between 1 and 24 one each face. Every number is featured exactly once. When he rolls, what is the probability that the number showing is a factor of 24? 1 3 integer between 1 and 24 is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 factor of 24 from 1 to 24 is 1, 2, 3, 4, 6, 8, 12, 24 Thus; 1/3