Math Answers

A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. The survey also showed that 5% of the consumers were dissatisfied and had specifically complained about work by Plumber X. Plumber X does 40% of the plumbing jobs in the community.

1. What is the probability that a randomly selected consumer in this community will obtain an unsatisfactory plumbing job, given that Plumber X did the work?

2. What is the probability that a randomly selected consumer in this will obtain a  

satisfactory plumbing job, given that Plumber X did the work?

We roll a pair of dice once and are given that the two numbers that occur are not the same. Compute the following probabilities:

• i) the sum is 7

• ii) the sum is 4

• iii) the sum is 12

A commuter passes through three traffic lights on the way to work. Each light is either red, yellow, or green. An experiment consists of observing the colour of the three lights.

• i) List the 27 possible outcomes in the sample space.

• ii) Let A be the event that all the colours are the same. List the outcomes of A.

• iii) Let B be the event that all the colours are different. List the outcomes of B.

• iv) Let C be the event that at least two lights are green. List the outcomes of C.

• v) List the outcomes in 𝐴 ⋂ 𝐶.

• vi) List the outcomes in 𝐴 ⋃ 𝐵.

• vii) List the outcomes in 𝐴 ⋂ 𝐶' .

• viii) List the outcomes in 𝐴' ⋂ 𝐶 .

• ix) Are events A and C mutually exclusive? Explain.

• x) Are events B and C mutually exclusive? Explain.

There are 9 eggs out of which 4 are bad. 3 eggs are chosen at random.

1) In how many ways can we choose the 3 eggs from among the 9 eggs?

2) In how many ways can we choose 3 good eggs?

3) What is the probability that all selected eggs are good?

4) In how many ways can we choose 3 bad eggs?

5) What is the probability that all 3 selected eggs are bad ones?

6) What is the number of pairs of good eggs?

7) In how many ways can we choose 3 eggs out of which 1 is bad?

8) What is the probability that exactly one egg is bad?

9) What is the probability that at least one egg is bad?

A person driving to work every day on a route with four traffic lights believes the following to be suitable probabilities for the number of red lights encountered on a trip. Let the random variable 𝑋 be the number of red lights encountered.

Let

A be the event that no red light is encountered with P(A) = 0.05,

B be the event that one red light is encountered with P(B) = 0.25,

C be the event that two red lights are encountered with P(C) = 0.36,

D be the event that three red lights are encountered with P(D) = 0.26,

and E be the event that four red lights are encountered with P(E) = 0.08.

1) Does these probabilities satisfy the axioms of probability?

2) What is the probability of encountering at least one red traffic light on a trip?

3) What is the probability of encountering more than two red traffic lights on a trip?

4) What is the probability of encountering at the most two red traffic lights on a trip?

Manen’s closet has three pairs of pants (black, white and green), two shirts (green and white) and two pairs of shoes (black and white).

• a) How many different outfits can be made?

• b)   Write down the sample space.

• c)   What is the probability that if you close your eyes and choose randomly, you would   

choose:

• (i) Pants and shoes with the same colour?

• (ii) Pants and shirts with the same colour?

• (iii) Pants, shoes and shirts with the same colour?

• (iv) Pants, shoes and shirts with the different colours?

If two dice are rolled, find the probability that:

• A. both show an odd number

• B. a sum of 7 shows

• C. a sum of 4 or 11 shows

• D. only the second die shows a 3.

In a sample of 500 families, 95 have an annual income of less than M80 000, 272 families have an annual salary of M80 000 to M150 000 and the remaining families have an annual income of more than M150 000. One family is randomly selected from these 500 families. Find the probability that this family has an annual income of:

• A) less than M80 000

• B) more than M150 000

• C) M80 000 to M150 000 or more than M150 000

• D) Show that the probability of the sample space is equal to 1

After graduating with a BCom degree, Tim had interviews with two companies A and B

Suppose that there is a 20% chance that he will be offered the job by company A and a 15%

chance that he will be offered a job with company B. Suppose that each company is unaware

that he has had an interview with the other company. What is the probability that he will be

offered a job by exactly one of the companies? (answer to 2 decimal places):

A box contains three two-sided coins of the same size and weight. Coin A is a standard

unbiased coin, while Coin B has two heads. Coin C is biased so that a tail is twice as likely to

occur as the head. A coin is randomly selected from the box, tossed and landed on "heads"

What is the probability that it is Coin C?