A Basketball Player Attempts Successive Free Throws Until He Succeeds $( 0.3 ) ^ { n }$

question 39

Short Answer

A basketball player attempts successive free throws until he succeeds in making a basket. Suppose the probability of success of each attempt is 0.7; thus, the probability of exactly n failures before the first success is $( 0.3 ) ^ { n }$ (0.7), n ≥ 0. What is the probability that the number of failures before the first successful free throw is odd? Enter just a reduced fraction.

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Definitions:

Linear Perspective

A technique in drawing and painting where parallel lines seem to converge as they recede towards a single point on the horizon, creating an illusion of depth.

Depth Cue

A signal in our environment, either binocular or monocular, that provides information about distance or depth.

Apparent Narrowing

The perceived reduction in size or scope of an object or concept, often as a result of specific conditions or perspectives.

Principle Of Closure

A psychological tendency to perceive a complete image even when the sensory information is incomplete, based on our brain's preference for simplicity and continuity.