IB Maths AI SL 4.6 Combined, Conditional and Independent Events

IB Mathematics: applications and interpretation guide, first assessment 2021

Practise representing combined events with tables, Venn or tree diagrams and applying union, intersection, conditional and independence rules with or without replacement.

How this is tested

select the appropriate union, intersection or complement from a table, Venn diagram or event description
calculate a conditional probability using the conditioning event as the restricted denominator
multiply updated branch probabilities without replacement or constant values when independent

[Maximum number: 12]

Hawksburn Aviation School offers three courses, flying, management and engineering. The following information was collected about the 50 students enrolled in courses at the school.
- 21 students are enrolled in the flying course only.
- 14 students are enrolled in both the flying course and the management course.
- Students enrolled in the engineering course are not enrolled in any other courses.
The information about all 50 students is presented in the following Venn diagram.

A student is selected randomly from this group.

(a)

Find the probability that

[ 4 ]

(i)

the student is enrolled in the management course, given that they are enrolled in the flying course.

Let F be the event that the student selected is enrolled in the flying course and M be the event that the student is enrolled in the management course.

[ 4 ]

(b)

State whether F and M are mutually exclusive. Justify your answer.

It is known that $\mathrm{P}(F \mid M)=0.7$ .

[ 2 ]

(c)

Find the value of x.

(d)

Find the value of y.

(e)

Write down the number of students enrolled in only one course.

Three students are randomly selected from the group of 50 to give a presentation.

[ 6 ]

How this is tested

Question 3

Question 3(a)

Question 3(a)(ii)

Question 3(b)

Question 3(c)(i)

Question 3(c)(ii)

Question 3(c)(iii)