Poisson with geometric or waiting time

A question is this type if and only if it involves finding probabilities related to waiting times or the number of trials until a Poisson event occurs.

3 questions

Edexcel S2 2015 January Q1
  1. The number of cars caught speeding per day, by a particular camera, has a Poisson distribution with mean 0.8
    1. Find the probability that in a given 4 day period exactly 3 cars will be caught speeding by this camera.
    A car has been caught speeding by this camera.
  2. Find the probability that the period of time that elapses before the next car is caught speeding by this camera is less than 48 hours. Given that 4 cars were caught speeding by this camera in a two day period,
  3. find the probability that 1 was caught on the first day and 3 were caught on the second day. Each car that is caught speeding by this camera is fined \(\pounds 60\)
  4. Using a suitable approximation, find the probability that, in 90 days, the total amount of fines issued will be more than \(\pounds 5000\)
Edexcel FS1 2019 June Q1
  1. A chocolate manufacturer places special tokens in \(2 \%\) of the bars it produces so that each bar contains at most one token. Anyone who collects 3 of these tokens can claim a prize.
Andreia buys a box of 40 bars of the chocolate.
  1. Find the probability that Andreia can claim a prize. Barney intends to buy bars of the chocolate, one at a time, until he can claim a prize.
  2. Find the probability that Barney can claim a prize when he buys his 40th bar of chocolate.
  3. Find the expected number of bars that Barney must buy to claim a prize.
AQA Further Paper 3 Statistics 2023 June Q2
1 marks
2 The time, \(T\) days, between rain showers in a city in autumn can be modelled by an exponential distribution with mean 1.25 Find the distribution of the number of rain showers per day in the city.
Tick ( \(\checkmark\) ) one box.
[0pt] [1 mark]
\includegraphics[max width=\textwidth, alt={}, center]{1e2fdd33-afa4-486f-a9e2-1d425ed14eee-03_108_113_1800_370}
DistributionMean
Exponential0.8
\includegraphics[max width=\textwidth, alt={}]{1e2fdd33-afa4-486f-a9e2-1d425ed14eee-03_108_113_1932_370}
Exponential1.25
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Poisson0.8
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Poisson1.25