Search & Filtering
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?
Find the mean and variance of a random variable X whose distribution has probability generating moment function is
pr / 1 − (1 − p)r 0 < p < 1
The average number of trailer trucks that passed by the South Road Properties in the morning is 60 trucks. What is the probability that exactly 65 trucks will pass by in the following morning?
‘Bhartdarshan’ is an Internet-based travel agency wherein customers can see videos of the
cities they plan to visit. The number of hits daily is a normally distributed random variable
with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits?
b. What is the probability of getting fewer than 9,000 hits?
A researcher claims that adult hogs fed a special diet will have an average weight of 200 pounds. A sample of 10 hogs has an average weight 198.2 pounds and standard deviation of 3.3 pounds. At a= 0.05, can the claim be rejected? Also, find the 95% confidence interval of the true mean?
