CAIE A-Level Mathematics A2 5.4.2 Geometric Distribution Questions

Practise modelling repeated trials with binomial and geometric distributions and interpreting their probabilities.

Exam points

identify and apply binomial and geometric distribution models
calculate probabilities for numbers of successes and waiting times
use distribution assumptions to solve repeated-trial problems

[Maximum number: 3]

The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg . On 10 % of days less than 16 kg of grapes are sold.

The mass of grapes sold on any day is independent of the mass sold on any other day.

12 days are chosen at random.

Find the probability that less than 16 kg of grapes are sold on more than 2 of these 12 days.

Let $X\sim\operatorname{Bin}(12,0.1)$ . Then
$P(X<3)=1-\left[\binom{12}{0}(0.1)^0(0.9)^{12}+\binom{12}{1}(0.1)(0.9)^{11}+\binom{12}{2}(0.1)^2(0.9)^{10}\right] =0.111.$

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CAIE A-Level Mathematics A2 5.4.2 Geometric Distribution Questions question 1