Answer:
8/11 probability
Step-by-step explanation:
Bayesian stats: you should estimate the prior probability that it’s raining on any given day in Seattle. If you mention this or ask the interviewer will tell you to use 25%. Then it’s straight-forward:
P(raining | Yes,Yes,Yes) = Prior(raining) * P(Yes,Yes,Yes | raining) / P(Yes, Yes, Yes)
P(Yes,Yes,Yes) = P(raining) * P(Yes,Yes,Yes | raining) + P(not-raining) * P(Yes,Yes,Yes | not-raining) = 0.25*(2/3)^3 + 0.75*(1/3)^3 = 0.25*(8/27) + 0.75*(1/27)
P(raining | Yes,Yes,Yes) = 0.25*(8/27) / ( 0.25*8/27 + 0.75*1/27 )
**Bonus points if you notice that you don’t need a calculator since all the 27’s cancel out and you can multiply top and bottom by 4.
P(training | Yes,Yes,Yes) = 8 / ( 8 + 3 ) = 8/11
