Question

Question 10
Let P(E) denote the probability of an event E happen-
ing. In an experiment, there are 4 possible outcomes
such that each of them are probable with distinct
probability. Each probability is a decimal number
0.CO, O.RO, O.NA and 0.19 where C,O,R,N and A
represent digits. If each of the first three probabilities
consist of the digit 5, find value of C (Given C>R).​

Answer 1

Given :   4 possible outcomes  such that each of them are probable with distinct  probability . Each probability is a decimal number

0.CO  +  0.RO  + 0.NA  + 0.19  . each of the first three probabilities  consist of the digit 5  C > R

To find :  Value of C

Solution:

0.CO  +  0.RO  + 0.NA  + 0.19  =  1

first three probabilities   consist of the digit 5

Let say  O  is not  5  Then

C & R has to be 5

Then Sum of probabilities will be greater then 1 hence not possible

so O has to be 5

Now  

as O = 5   then A  Has to be  1     (as 5 + 5 + A + 9 should end with 0)

A is 1  hence N has to be 5

So we get

0,C5 + 0.R5 + 0.51 + 0.19  = 1

=> 0.C5 + 0.R5  = 0.3

=> 0.C + 0.R  = 0.2

Possible values of  C  & R

are  2 & 0  as C  > R

Hence Value of C  = 2

Probabilities are

0.25   , 0.05  + 0.51 + 0.19  

Value of C  = 2

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