(b) Suppose that, on average, the number of

Answered question

2022-03-10

(b) Suppose that, on average, the number of car accidents in Hong Kong are 6 per day (which has 24 hours).i. Determine the probability that at least x accidents will occur in 12 hour period. (4 marks) ii. In a two days, if there were 8 car accidents in Hong Kong, what is the probability that 2 accidents have occurred in the first 12 hours of the two days?

Answer & Explanation

nick1337

nick1337

Expert2022-03-22Added 777 answers

b) The number of car accidents here is modelled as:
X = Poisson (M = 6)

i) The probability of at least X accidents in a 12 hour period here is computed as:
P(X x) for X = Poisson (M = 3) as mean in 12 hour period would be 6/2 = 3

=1-P(X<x)

=1-i=0x-13ii!*(e-3)

This is the required probability here.

 

ii) For a 2 day period, given that there were 8 car accidents, the probability that there were 2 accidents in the first 12 hours is computed here as:

P(X = 2) P(Y = 6) / P(X + Y) = 8 Where X = poisson(3) and Y = poisson(9)

=322e-3*966!e-91288!e-12

=0.3115

Therefore 0.3115 is the required probability here.

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