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
Answers
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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