IB · Mathematics: Analysis & Approaches SL & HL · Statistics & probability

Binomial distribution: IB Mathematics: Analysis & Approaches questions with answers

Free Binomial distribution questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Statistics & probability. Each question has the answer and the marking points an examiner would look for.

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Binomial distribution practice questions

Question 1Structured · 6 marksA* challenge

A random variable X ~ B(n, p) has mean 15 and variance 6.

(a)

Find the value of p and the value of n.

[4]
(b)

Find P(X ≤ 14).

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)p = 0.6, n = 25
np = 15, np(1 − p) = 6 (M1)
1 − p = 0.4 A1
p = 0.6 A1
n = 25 A1
4
(b)0.414
binomial CDF (M1)
0.414 A1
2
Question 2Structured · 4 marksA* challenge

The probability that a component is faulty is 0.1. Find the least number of components that must be tested so that the probability of finding at least one faulty component is greater than 0.95.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
29
1 − (1 − 0.1)n > 0.95 (M1)(A1)
solving (M1)
29 A1
4
Question 3Structured · 7 marks

In a large school, 35% of students walk to school. A random sample of 12 students is chosen. Let X be the number of these students who walk to school.

(a)

Find P(X = 4).

[2]
(b)

Find P(X ≥ 6).

[2]
(c)

Find the least number of students that must be sampled so that the probability that at least one of them walks to school is greater than 0.99.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.237
X ~ B(12, 0.35) (M1)
0.237 A1
2
(b)0.213
1 − P(X ≤ 5) (M1)
0.213 A1
2
(c)11
1 − 0.65n > 0.99 (M1)
n > 10.7 (A1)
11 A1
3
Question 4Structured · 6 marks

The probability that a seed germinates is 0.35. 12 seeds are planted.

(a)

Find the probability that exactly 4 germinate.

[2]
(b)

Find the probability that more than 4 germinate.

[2]
(c)

Find the expected number of seeds that germinate and the variance.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)0.237
B(12, 0.35) (M1)
0.237 A1
2
(b)0.417
1 − P(X ≤ 4) (M1)
0.417 A1
2
(c)4.20; 2.73
E = 4.20 A1
Var = 2.73 A1
2
Question 5Structured · 6 marksA* challenge

A random variable X ~ B(n, p) has mean 4.8 and variance 2.88.

(a)

Find the value of p and the value of n.

[4]
(b)

Find P(X ≤ 4).

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)p = 0.4, n = 12
np = 4.8, np(1 − p) = 2.88 (M1)
1 − p = 0.6 A1
p = 0.4 A1
n = 12 A1
4
(b)0.438
binomial CDF (M1)
0.438 A1
2
Question 6Structured · 4 marksA* challenge

The probability that a component is faulty is 0.2. Find the least number of components that must be tested so that the probability of finding at least one faulty component is greater than 0.95.

[4]
Show answers and mark scheme
PartAnswer and marking pointsMarks
14
1 − (1 − 0.2)n > 0.95 (M1)(A1)
solving (M1)
14 A1
4

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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