IB Maths AI SL 4.8 Binomial distribution Question Bank

Practise IB Mathematics SL/HL 4.8 by applying binomial distribution methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 6]

A large international sports tournament tests their athletes for banned substances.
They interpret a positive test result as meaning that the athlete uses banned substances. A negative result means that they do not.
The probability that an athlete uses banned substances is estimated to be 0.06 .
If an athlete uses banned substances, the probability that they will test positive is 0.71 .
If an athlete does not use banned substances, the probability that they will test negative is 0.98 .

(a)

Calculate the probability that none of the athletes in Team X will test positive.

[ 4 ]

$\quad p=0.02$ OR p=0.98
recognition of binomial probability with n=20

\mathrm{P}(X=0) \text { OR } \mathrm{P}(X=20)

0.668 (0.667607...)

Note: Award (A1)(M1)(M1)A0 for an answer of 0.667 .
$0.98^{20}=0.668(0.667607 \ldots)$ is awarded full marks.

(b)

Determine the probability that more than 2 athletes in Team X will test positive.

[ 2 ]

$\quad \mathrm{P}(X \geq 3)$ OR $\mathrm{P}(X \leq 17)$
0.00707 (0.00706869...)

Note: Award (M1)A0 for an answer of 0.00706 .
FT from their value of p in part (d)

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SL 4.8—Binomial distribution question 1

Question (a)

Question (b)