In these lessons, we will learn how to solve a variety of probability problems.
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Here we shall be looking into solving probability word problems involving:
We will now look at some examples of probability problems.
Example:
At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are lorries.
If every vehicle is equally likely to leave, find the probability of:
a) a van leaving first.
b) a lorry leaving first.
c) a car leaving second if either a lorry or van had left first.
Solution:
a) Let S be the sample space and A be the event of a van leaving first.
n(S) = 100
n(A) = 30
Probability of a van leaving first:
b) Let B be the event of a lorry leaving first.
n(B) = 100 – 60 – 30 = 10
Probability of a lorry leaving first:
c) If either a lorry or van had left first, then there would be 99 vehicles remaining,
60 of which are cars. Let T be the sample space and C be the event of a car leaving.
n(T) = 99
n(C) = 60
Probability of a car leaving after a lorry or van has left:
Example:
A survey was taken on 30 classes at a school to find the total number of left-handed students in
each class. The table below shows the results:
No. of left-handed students | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|
Frequency (no. of classes) | 1 | 2 | 5 | 12 | 8 | 2 |
A class was selected at random.
a) Find the probability that the class has 2 left-handed students.
b) What is the probability that the class has at least 3 left-handed students?
c) Given that the total number of students in the 30 classes is 960, find the probability
that a student randomly chosen from these 30 classes is left-handed.
a) Let S be the sample space and A be the event of a class having 2 left-handed students.
n(S) = 30
n(A) = 5
b) Let B be the event of a class having at least 3 left-handed students.
n(B) = 12 + 8 + 2 = 22
c) First find the total number of left-handed students:
No. of left-handed students, x | 0 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|
Frequency, f (no. of classes) | 1 | 2 | 5 | 12 | 8 | 2 |
fx | 0 | 2 | 10 | 36 | 32 | 10 |
Total no. of left-handed students = 2 + 10 + 36 + 32 + 10 = 90
Here, the sample space is the total number of students in the 30 classes, which was given as 960.
Let T be the sample space and C be the event that a student is left-handed.
n(T) = 960
n(C) = 90
Example:
ABCD is a square. M is the midpoint of BC and N is the midpoint of CD. A point is selected at
random in the square. Calculate the probability that it lies in the triangle MCN.
Let 2x be the length of the square.
Area of square = 2x × 2x = 4x^{2}
Area of triangle MCN is
This video shows some examples of probability based on area.
The following video shows some examples of probability problems. A few examples of calculating the probability of simple events.
Example:
This video introduces probability and gives many examples to determine the probability of basic events.
Example:
A bag contains 8 marbles numbered 1 to 8
a. What is the probability of selecting a 2 from the bag?
b. What is the probability of selecting an odd number?
c. What is the probability of selecting a number greater than 6?
Using a standard deck of cards, determine each probability.
a. P(face card)
b. P(5)
c. P(non face card)
This video shows how to evaluate factorials, how to use permutations to solve probability problems, and how to determine the number of permutations with indistinguishable items.
A permutation is an arrangement or ordering. For a permutation, the order matters.
Examples:
This video shows how to evaluate combinations and how to use combinations to solve probability problems.
A combination is a grouping or subset of items. For a combination, the order does not matter.
Examples:
This video explains how to determine the probability of different events. This can be found that can be found using combinations and basic probability.
A group of 10 students made up of 6 females and 4 males form a committee of 4.
What is the probability the committee is all male?
What is the probability that the committee is all female?
What is the probability the committee is made up of 2 females and 2 males?
This video explains the counting principle and how to determine the number of ways multiple independent events can occur.
Examples:
This video shows how to determine the probability of a union of two events.
Examples:
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
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