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    An indoor tennis centre has five courts which are booked by members of the public, usually over the telephone.

    (a) It has been found that demand for courts in each off-peak hour, i.e. between 9am and 4pm, has a Poisson distribution with a mean of 4.
    (i) What is the probability that none of the courts are booked between 10am and 11am on a particular day?
    (ii) What is the probability that all five courts are booked between 10am and 11am on a particular day?
    (iii) What is the probability that none of the courts are booked for exactly three of the off-peak hours on a particular day?
    (iv) What is the probability that all 5 courts are booked for at least 5 of the off-peak hours?

    I got

    (1) 0.01832
    (2) 0.15629
    Is that correct?

    And haven't got a clue, haow to start (3) or (4) need help please :shifty:

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    I don't have a calculator handy so I can't check 1) and 2).

    For iii) and iv), a small hint is that you're going to need the Binomial distribution. A larger hint:

    Spoiler:
    Show
    X ~ B(7, p), where p is the probability of no courts being booked in any given hour (or "successes" ), and there are 7 off peak hours in a day ("trials" ).
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    (Original post by tommm)
    I don't have a calculator handy so I can't check 1) and 2).

    For iii) and iv), a small hint is that you're going to need the Binomial distribution. A larger hint:

    Spoiler:
    Show
    X ~ B(7, p), where p is the probability of no courts being booked in any given hour (or "successes" ), and there are 7 off peak hours in a day ("trials" ).
    Ok I get your point. But shouldn't n=8, from 9am to 4 pm is eight hours, If I am not mistaken. thus X~B(8,p).

    Also is the p for (3) Probability of none courts booked within an hour?

    Same for the (4) but for all five booked?

    Thank yo
 
 
 
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