APFIVE Geometric Distribution Parameter Change
An experiment: Diogenes encounters men sequentially in ancient Greece, where the probability of an honest man is $$0.12$$ and the probability that the first honest man is found on the third encounter is computed using the geometric distribution. What would happen if the probability of honesty increases to $$0.15$$, in terms of the probability that the first honest man is encountered on the third trial?
TABLE: Geometric Distribution Parameters
| Parameter | Original Value | Modified Value |
|---|---|---|
| p (honesty) | 0.12 | 0.15 |
| Trial | 3 | 3 |
A
It becomes exactly equal to $$15\%$$.
B
It increases to roughly $$10.84\%$$.
C
It remains the same as before.
D
It decreases to less than $$5\%$$.
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