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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.
On any one day, there are 1000 cars on the roads of a small town. The probability of any one
car crashing on a given day is 0.002. The town has three paramedics. Whenever an accident
occurs, a paramedic goes to the scene and remains there for the rest of the day caring for
the accident victims. Assume that the safety record of any one car is independent of that of
all the other cars.
If all three paramedics are called out to the different accident scenes, then victims at any
additional accident scenes would not be able to receive medical attention. The exact
probability that accident scenes on a particular day will not be able to receive medical
attention by any of the town's three paramedics is (to 4 decimal places):
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
a) Give an example of an experiment. Identify the experimental units? What are the possible outcomes of the experiment?
ai) What are the two types of experiments? Give an example of each.
b) What are the properties of experiments?
c) Think of any experiment/trial. What are the possible outcomes? What ple points? From your trial, define the possible events and write down their elements.
d) Suppose we ask the next person we meet on the street in which month his/her birthday falls. What is the sample space?
e) Let A be the event that the month has 31days. What are the elements of A?
f) Let B be the event that the month has a letter “r” in their full names. What are the elements of B?
g) What is A intersection B?
h) What is the union of A and B?
i) Is B a subset of A?
j) Are A and B mutually exclusive?
1. Give an example of an experiment. Identify the experimental units? What are the possible outcomes of the experiment?
2. What are the two types of experiments? Give an example of each.
3. What are the properties of experiments?
4. Think of an experiment/trial. What are the possible outcomes? What are the sample points? From your trial, define the possible events and write down their elements.
#339914 on Dec 2023