Math Answers

Thirty people, who are of the same age and the same health status, are

insured with the same insurance company. Using life tables, the company

estimates that the probability for a randomly chosen person among these 30

to be alive in 15 years from now is 0:8.

(i) What is the probability that not all 30 people will be alive in 15 years time?

(ii) What is the probability that at least one person will be alive?

Verify that each of the following statements is a false statement by finding a counterexample for each.

1. xx=1
2. x+33=x+1
3. x2+16=x+4

The probability that a car is stolen when it is parked overnight in an unsafe

area of a city is 10%. If there are 12 cars parked on a particular street of that

area, what is the probability that during a night

(i) no car is stolen?

(ii) at most two cars are stolen?

(iii) at least nine cars are stolen?

Wanda, Loki, Natasha, and Stephen were recently elected as the new class officers (president, vice

president, secretary, treasurer) of the sophomore class at Marvel College. From the following clues,

determine which position each holds.

1. Stephen is younger than the president but older than the treasurer.

2. Wanda and the secretary are both the same age, and they are the youngest members of the

group.

3. Natasha and the secretary are next door neighbors.

Determine whether each of the following arguments is an example of inductive reasoning or deductive

reasoning.

a. All Janet Evanovich novels are worth reading. The novel To the Nines is a Janet Evanovich

novel. Thus To the Nines is worth reading.

b. I know I will win a jackpot on this slot machine in the next 10 tries, because it has not paid out

any money during the last 45 tries.

Use deductive reasoning to show that the following procedure produces a number that is three times

the original number. Procedure: Pick a number. Multiply the number by 6, add 10 to the product, divide

the sum by 2, and subtract 5. Hint: Let n represent the original number.

Use inductive reasoning to predict the most probable next number in the following lists.

a) 5, 10, 15, 20, 25, ?

b) 2, 5, 10, 17, 26, ?

Consider the following procedure: Pick a number. Multiply the number by 9, add 15 to the product,

divide the sum by 3, and subtract 5. Complete the above procedure for several different numbers. Use

inductive reasoning to make a conjecture about the relationship between the size of the resulting number

and the size of the original number.

A TV manufacturer claims that the life span of its regular TV sets is longer than 10 years with a standard deviation of 1.5 years. Using a random sample of their 16 TV sets, the average life span is found to be 11.5 years. Test the hypothesis that the TV sets' life span is longer than 10 years at a = 0.01.

A chemical company alleged that the average weight of its bag of chemical is 50 kgs. with a standard deviation of 0.9 kg. A sample of 29 bags was taken and revealed a mean weight of 48.1 kgs. Shall we accept the allegation of the chemical company? Use a = 0.01.