Question

it is well-known fact that 15 percent of Great Pyrenees dogs drool excessively. what is the probability that if you pet all the different Great Pyrenees at a Great Pyrenees fan club event, the eight dog you pet will be the first that drools excessively?

Answer 1

Percentage of Great Pyrenees dogs drool excessively = 15%

Probability of a Great Pyrenees dogs drool excessively : p = 15/100 = 0.15

Probability that the eight dog you pet will be the first that drools excessively.

S: Success : Dog that drolls excessively

F : Failure : Dog that does not droll excessively

Probability of success : p = 0.15

Probability of failure : 1-p = 1-0.15 = 0.85

Eight dog you pet will be the first that drools excessively which means first seven dog do not drool excesively andd eight dog drool excessively i.e

seven failures and then a Success i.e FFFFFFFS

P(FFFFFFFS) = P(F)⁷ P(S) = (1-p)⁷p = 0.85⁷ x 0.15 = 0.3206 x 0.15= 0.0481

Probability that the eight dog you pet will be the first that drools excessively = 0.0481

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Applying Geometric Distribution which states,

The geometric distribution gives the probability that the first occurrence of success requires k independent trials, each with success probability p. If the probability of success on each trial is p, then the probability that the kth trial (out of k trials) is the first success is

for k = 1, 2, 3, ....

For the given problem, k=8; p=0.15

Probability that the eight dog you pet will be the first that drools excessively = 0.0481