1st q:

if (1+3p)/3,(1-p)/4 and (1-2p)/2 r d probailities of 3 mutually xclusive events show dat 1/3<=p<=1/2.

2nd q:

if k objects r distributed in random among k persons ,find d probability dat at least one of them will nt gt anything.

QI)

probailities of each event lies between [0,1]

so , 1-2p >=0

      p=<1/2  ....(1)

also for mutually exclusive events, sum of probabilities is 1

(1+3p)/3 + (1-p)/4 + (1-2p)/2 =<1

(13-3p)/12 =<1

p>=1/3

so , 1/3 =< p =< 1/2

QII )

no of ways of distributing r objects among k persons is : kCr

no of ways of distributing r objects among (k-1) persons leaving a single person is : (k-1)Cr

probability = (k-1)Cr /kCr

                = (k-r)/k

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regards

Ramesh

but the question reads "k objects r (ARE) distributed in random among k persons", why is this r for in your solution?