Posted by **Anonymous** on Friday, April 30, 2010 at 2:09am.

The public transport system is aware that one person in twenty does not buy a ticket for their trip. The manager decides to challenge 200 travelling people as to charger they have a valid ticket or not.

(a) calculate the probabilty that everyone had a ticket,

(b) calculate the probabilty that at most 3 people had no ticket, and

(c) calculate the probabilty that between 7 and 14 (inclusive) had no ticket. I thought binomial? But then 200 is too big for it? Thanks for any help!

- Probability -
**Reiny**, Friday, April 30, 2010 at 8:09am
Agree that the numbers are enourmous, so I will leave answers in notation form

a) prob of having ticket = 19/20

So prob that 200 people have a ticket = (19/20)^200

b) prob that at most 3 will have no tickets

= prob(3 no ticket) + prob(2 no ticket) + prob(1 no ticket) + prob(0 no ticket)

= C(200,3)(1/20)^3(19/20)^197 + C(200,2)(1/20)^2(19/20)198 + ...

c) C(200,7)(1/20)^7(19/20)^193 + ... + C(200,14)(1/20)^14(19/20)^186

e.g. C(200,14)(1/20)^14(19/20)^186 = .0517578

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