Probability: IB Mathematics: Applications & Interpretation questions with answers
Free Probability questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.
On any day the probability that it rains is 0.25. If it rains, the probability that Ana is late is 0.7. If it does not rain, the probability that she is late is 0.15.
(a)
Find the probability that Ana is late on a given day.
[2]
(b)
Given that Ana is late, find the probability that it rained.
[2]
(c)
Find the probability that Ana is late on exactly one of two days.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.287
0.25 × 0.7 + 0.75 × 0.15 (M1) 0.287 A1
2
(b)
0.609
0.175/0.287 (M1) 0.609 A1
2
(c)
0.410
2 × 0.287 × 0.713 (M1) 0.410 A1
2
Question 2Structured · 7 marksA* challenge
For events A and B, P(A) = 0.5, P(B) = 0.4 and P(A | B) = 0.6.
(a)
Find P(A ∩ B).
[2]
(b)
Find P(A ∪ B).
[2]
(c)
Find P(B | A′).
[2]
(d)
Determine whether A and B are independent, giving a reason.
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.240
P(A | B) × P(B) (M1) 0.240 A1
2
(b)
0.660
P(A) + P(B) − P(A ∩ B) (M1) 0.660 A1
2
(c)
0.320
P(B ∩ A′)P(A′) = 0.1600.500(M1) 0.320 A1
2
(d)
not independent
P(A | B) = 0.6 ≠ P(A) = 0.5, so not independent R1
1
Question 3Structured · 6 marks
A survey asked students whether they prefer online or printed books.
Online
Printed
Year 11
21
13
Year 12
18
24
Table 3.1
(a)
Find the probability that a randomly chosen student prefers online books.
[2]
(b)
Given that a student is in Year 12, find the probability that they prefer printed books.
[2]
(c)
Determine whether preferring online books is independent of year group. Justify your answer.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
3976
21 + 1876(M1) 3976A1
2
(b)
47
2442(M1) 47A1
2
(c)
not independent
P(online | Year 11) = 0.618, P(online) = 0.513 R1 not equal, so not independent A1
2
Question 4Structured · 3 marks
A survey asked people whether they prefer tea or coffee.
Tea
Coffee
Male
22
19
Female
17
29
Table 4.1
(a)
Find the probability that a randomly chosen person is female and prefers coffee.
[1]
(b)
Find the probability that a person prefers tea, given that they are male.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
13
13A1
1
(b)
2241
conditional (M1) 2241A1
2
Question 5Structured · 6 marks
In a class of 43 students, 19 study French (F), 18 study Spanish (S) and 9 study both.
(a)
Find the number of students who study neither.
[1]
(b)
Find P(F ∪ S) and P(S | F).
[3]
(c)
Determine whether F and S are independent.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
15
15 A1
1
(b)
2843, 919
2843A1 conditional on F (M1) 919A1
3
(c)
not independent
P(F)P(S) = 0.185, P(F ∩ S) = 0.209 M1 not equal, so not independent A1
2
Question 6Structured · 6 marksA* challenge
On any day the probability that it rains is 0.3. If it rains, the probability that Ana is late is 0.6. If it does not rain, the probability that she is late is 0.1.
(a)
Find the probability that Ana is late on a given day.
[2]
(b)
Given that Ana is late, find the probability that it rained.
[2]
(c)
Find the probability that Ana is late on exactly one of two days.
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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in