Homework Answers

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?

Five accounts are randomly sampled without replacement from a box of forty accounts. The

box contains thirty accounts that have a debit balance. What is the probability of selecting at

least one account with a credit balance?