• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Question and answer bank question 1.10

A

alyaaredha

Member
in question 1.10 part i)b) we are asked to find he probability he passes the 5th exam, given that he fails the first three. The question seems pretty straightforward and I would assume that you calculate the probability using these 2 paths :
F-F-F-F-P or F-F-F-P-P getting (1-beta^2)(beta*alpha+(1-beta)*beta). The answer given is just (beta*alpha+(1-beta)*beta) and i can't seem to see why. Could anyone let me know where I went wrong?
Thank you!!
Aliaa
 
The paths you determined are correct:
The probability of first path is as below:
it is given that he fails first three so the Prob. of failing the fourth given he failed in third is (1-beta). Further, Prob. of passing the fifth given failed in fourth is beta. So the total probability of first path is beta*(1-beta).
Similarly, Prob. of second path is alpha*beta.
 
Back
Top