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a. For each of the following statements, say whether it is true or false. i. There are in total 10-P(9,4) possible different number plates consisting of 6 digits (0 to 9) with exactly 2 of the same digit. ii. Three standard (6-sided) dice are rolled. One is red, one is blue, and one is green. If the particular number showing on each coloured die is important, then there are in total 6'possible different outcomes. i. A bag contains 10 black and 12 white balls and each ball is considered distinguishable from each other. There are in total C(10,5)C(12,3)-C(10,6)C(12,2) different ways to select 8 balls so that exactly 5 or 6 are black. iv. Two 6-sided fair dice are rolled. The probability that at least one of the dice is 6, is . v. Tossing a fair coin and getting a head is mutually exclusive from rolling a 6-sided die and getting a 5.

a. For each of the following statements, say whether it is true or false. i. There are in total 10-P(9,4) possible different number plates consisting of 6 digits (0 to 9) with exactly 2 of the same digit. ii. Three standard (6-sided) dice are rolled. One is red, one is blue, and one is green. If the particular number showing on each coloured die is important, then there are in total 6'possible different outcomes. i. A bag contains 10 black and 12 white balls and each ball is considered distinguishable from each other. There are in total C(10,5)C(12,3)-C(10,6)C(12,2) different ways to select 8 balls so that exactly 5 or 6 are black. iv. Two 6-sided fair dice are rolled. The probability that at least one of the dice is 6, is . v. Tossing a fair coin and getting a head is mutually exclusive from rolling a 6-sided die and getting a 5.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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a. For each of the following statements, say whether it is true or false. i. There are in total 10-P(9,4) possible different number plates consisting of 6 digits (0 to 9) with exactly 2 of the same digit. ii. Three standard (6-sided) dice are rolled. One is red, one is blue, and one is green. If the particular number showing on each coloured die is important, then there are in total 6° possible different outcomes. iii. A bag contains 10 black and 12 white balls and each ball is considered distinguishable from each other. There are in total C(10,5)C(12,3)-C(10,6)C(12,2) different ways to select 8 balls so that exactly 5 or 6 are black. iv. Two 6-sided fair dice are rolled. The probability that at least one of the dice is 6, is . v. Tossing a fair coin and getting a head is mutually exclusive from rolling a 6-sided die and getting a 5. b. A necklace is to be formed by threading 8 beads on a circle of string. The beads are taken from a bag containing 14 different beads. How many options are there for a necklace if the knot holding the string together is not visible? Explain your ar answer. c. An insurance company issues car insurance, homeowner insurance, and life insurance. Of the claims the company pays, 50% are car, 40% are homeowner, and 10% are life. The company is primarily concerned with claims over RM50,000 that it pays. History has shown that 10% of car claims, 30% of homeowner claims, and 90% of life insurance claims exceed RM50,000. i. What percentage of claims paid by this company exceed RM50,000? ii) Given that this company pays a claim over RM50,000, what is the probability that it is a homeowner claim?
Transcribed Image Text:a. For each of the following statements, say whether it is true or false. i. There are in total 10-P(9,4) possible different number plates consisting of 6 digits (0 to 9) with exactly 2 of the same digit. ii. Three standard (6-sided) dice are rolled. One is red, one is blue, and one is green. If the particular number showing on each coloured die is important, then there are in total 6° possible different outcomes. iii. A bag contains 10 black and 12 white balls and each ball is considered distinguishable from each other. There are in total C(10,5)C(12,3)-C(10,6)C(12,2) different ways to select 8 balls so that exactly 5 or 6 are black. iv. Two 6-sided fair dice are rolled. The probability that at least one of the dice is 6, is . v. Tossing a fair coin and getting a head is mutually exclusive from rolling a 6-sided die and getting a 5. b. A necklace is to be formed by threading 8 beads on a circle of string. The beads are taken from a bag containing 14 different beads. How many options are there for a necklace if the knot holding the string together is not visible? Explain your ar answer. c. An insurance company issues car insurance, homeowner insurance, and life insurance. Of the claims the company pays, 50% are car, 40% are homeowner, and 10% are life. The company is primarily concerned with claims over RM50,000 that it pays. History has shown that 10% of car claims, 30% of homeowner claims, and 90% of life insurance claims exceed RM50,000. i. What percentage of claims paid by this company exceed RM50,000? ii) Given that this company pays a claim over RM50,000, what is the probability that it is a homeowner claim?
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