IB Math HL – Probability & Combinatorics
Questions and Answers
1. Permutations Combinations – IB Mathematics HL
How can we find the number of possible choices for choosing a sub-committee of five persons consisting of the chairperson, secretary and three ordinary membersfrom a committee of 40 people?
Solution
Permutations, Combinations – IB Maths HL
The chairperson can be chosen by ways
The secretary can be chosen by ways
And the three ordinary members can be chosen by ways
So, the members of this sub-committee can be chosen by
ways.
2. Permutations Combinations – IB Math HL
In a class of 12 students, 4 are male and 8 are female. How can we find the number of committees of 5 members can be formed containing 2 males and 3 females?
Solution
Permutations, Combinations – IB Maths HL
The males can be chosen by ways
The females, can be chosen by ways
So, the members of this committee can be chosen by
ways.
3. Permutations Combinations Probability- IB Mathematics HL
How can we find the number of different arrangements of the letters of the word “LONDON”? and how can we calculate the probability of the event that the middle two letters both are N’s?
Solution
Permutations, Combinations, Probability – IB Maths HL
The number of different arrangements of the six letters from which there are two pairs of same letters is given by the following formula
Since the two N’s are located in the middle of the word there are ways to arrange the remaining 4 letters from which there are two O,s.
So, the probability equals to
4. Probability- IB Mathematics HL
How can we find the probability if A and B are two events such that
,
and
?
Solution
Probability – IB Mathematics HL – IB maths HL
We know that
Finally, we have
5. Conditional Probability – IB Mathematics HL
How can we find the probability if A and B are two events such that
,
and
?
Solution
Probability – IB Mathematics HL – IB maths HL
From conditional probability formula we have that
Finally, we have that