A Thumb Tack Is Tossed Until It fiRst Lands with Its

question 20

Essay

A thumb tack is tossed until it first lands with its point down, at which time no more tosses are made. On each toss, the probability of the tack's landing point down is $1 / 3$
(a) What is the probability that exactly five tosses are made?
(b) What is the expected number of tosses?

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Definitions:

Spinothalamic Tract

A sensory pathway originating in the spinal cord that transmits information about pain and temperature to the thalamus in the brain.

Fasciculus Gracilis Tract

A sensory pathway in the spinal cord that conveys information about touch and proprioception from the lower body to the brain.

Spinocerebellar Pathway

A neural pathway that carries information from the spine to the cerebellum, crucial for coordinating movement.

Tectospinal Tract

A neural pathway originating in the midbrain that controls neck and upper limb movements in response to visual stimuli.