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2.4.1 Discrete distributions and the binomial

Question 7

The probability that a car fails an emissions test is 0.18, independently of every other car. A random sample of $n\,$ cars is tested.

Show that the probability that at least one of the $n\,$ cars fails is $1 - 0.82^n$ .

[2]

Find the smallest value of $n\,$ for which this probability exceeds 0.99.

[3]

State one assumption needed for the binomial model to be appropriate here.

[1]

Markscheme

2.4.1 Discrete distributions and the binomial Questions

A Level
Maths
2.4.1 Discrete distributions and the binomial

39 exam-style questions on AQA A Level Maths 2.4.1 Discrete distributions and the binomial. Each one has a worked solution and a mark scheme showing where the marks go.

2.4.1 Discrete distributions and the binomial

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2.4.1 Discrete distributions and the binomial

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Question 7

The probability that a car fails an emissions test is 0.18, independently of every other car. A random sample of $n\,$ cars is tested.

Show that the probability that at least one of the $n\,$ cars fails is $1 - 0.82^n$ .

[2]

Find the smallest value of $n\,$ for which this probability exceeds 0.99.

[3]

State one assumption needed for the binomial model to be appropriate here.

[1]

Markscheme

2.4.1 Discrete distributions and the binomial Questions

A Level
Maths
2.4.1 Discrete distributions and the binomial

39 exam-style questions on AQA A Level Maths 2.4.1 Discrete distributions and the binomial. Each one has a worked solution and a mark scheme showing where the marks go.