SOLUTION: 8- When an experiment is performed, one and only one of the events A₁, A₂ and A₃ will occur. Find P (A₁), P (A₂) and P (A₃) under each of the fo

Algebra ->  Probability-and-statistics -> SOLUTION: 8- When an experiment is performed, one and only one of the events A₁, A₂ and A₃ will occur. Find P (A₁), P (A₂) and P (A₃) under each of the fo      Log On


   

Question 427858: 8- When an experiment is performed, one and only one of the events A₁, A₂ and A₃ will occur. Find P (A₁), P (A₂) and P (A₃) under each of the following assumptions:
a) P(A₁) = P(A₂) = P(A₃)
b) P(A₁) = P(A₂) and P(A₃) = 1/2
c) P(A₁) = 2P(A₂) = 3P(A₃)
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Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

Here these events are mutually exclusive events..
a)
P(A1) = P(A2) = P(A3)
so, P(A1) = P(A2) = P(A3)= 1/3


b)
P(A1) + P(A2) = 1 - P(A3) = 1-1/2 = 1/2
so, P(A1) = P(A2) = 1/4

c)
P(A1) = 2 P(A2) = 3 P(A3)
we can write, P(A2)= P(A1)/2
P(A3) = P(A1)/3
now, P(A1)+ P(A1)/2+ P(A1)/3 = 1
=> 11/6 * P(A1) = 1
=> P(A1) = 6/11
using value of P(A1) we find...
P(A2) = 3/11
P(A3) = 2/11