John and Mary are friends at Spar and whilst working under pressure, a table is deleted in their SQL database. They are asked about who deleted the table. John tends to tell the truth 65% of the time while Mary tends to tell the truth 95% of the time.
What is the likelihood that one is lying while the other is truthful?
Answers
likelihood that one is lying while the other is truthful = 36.5% if John tends to tell the truth 65% & Mary tends to tell the truth 95% of the time
Step-by-step explanation:
John tends to tell the truth 65%
=> John telling Truth probability = 0.65
=> John lying probability = 1 - 0.65 = 0.35
Mary tends to tell the truth 95%
=> John telling Truth probability = 0.95
=> John lying probability = 1 - 0.95 = 0.05
Likelihood that one is lying while the other is truthful
= John Truth * Mary Lying + Mary Truth * John lying
= (0.65)(0.05) + (0.35)(0.95)
= 0.0325 + 0.3325
= 0.365
= 36.5%
Another Way
= 1 - Both lying - Both truthful
= 1 - (0.35)(0.05) -(0.65)(0.95)
= 1 -( 0.0175 + 0.6175)
= 1 - (0.635)
= 0.365
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