Question

On any given day Gary is either cheerful (C), so-so (S), or glum (G). If he is cheerful
today, then he will be C, Sor G tomorrow with respective probabilities 0.5, 0.4 and 0.1. If
he is feeling so-so today, then he will be C, S, or G tomorrow with probabilities 0.3, 0.4,
0.3. If glum today, then he will be C, S or G tomorrow with probabilities 0.2, 0.3 and 0.5.
Gary is currently I cheerful mode. What is the probability that he is not in a glum mood
on any of the following three days?
A
B)
C)
A)
0.585
0.523
0.423
0.486​

Answer 1

Given :  On any given day Gary is either cheerful (C), so-so (S), or glum (G) . Probabilities are given . Gary is in cheerful mood

To find :   probability that he is not in a glum mood  on any of the following three days

Solution:

Gary is currently in cheerful mode.

on next 3 days he is not in a glum mood

8 possible cases

CCC  -   (0.5)(0.5)(0.5)  =  0.125

CCS  -    (0.5)(0.5)(0.4)  = 0.1

CSC  -   (0.5)(0.4)(0.3)  = 0.06

CSS -    (0.5)(0.4)(0.4)  =  0.08

SCC   -  (0.4)(0.3)(0.5)  = 0.06

SCS   -   (0.4)(0.3)(0.4)  = 0.048

SSC  -    (0.4)(0.4)(0.3)  = 0.048

SSS  -    (0.4)(0.4)(0.4)  =  0.064

Total  =    0.585

Option A  is correct

Gary is currently I cheerful mode. Probability that he is not in a glum mood  on any of the following three days =  0.585

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