Suppose a Man Has Ordered Twelve 1-Gallon Paint Cans of a Particular

question 159

Multiple Choice

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let $x =$ the number of the paint cans selected that are defective. Unknown to the man, $x$ follows a hypergeometric distribution. Find the probability that none of the four cans selected contains an incorrect mix of paint.

• A) 0.01818
• B) 0.25455
• C) 0.21818
• D) 0.50909

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Definitions:

Gametophyte

The sexual phase in the life cycle of plants and algae that produces gametes, typically through mitosis.

Spores

Asexual reproductive or resting cells capable of developing into a new organism without fusion with another cell, often seen in bacteria, fungi, and plants.

Haploid Spores

Single-celled reproductive units produced by plants, fungi, and some protozoa that contain only one set of chromosomes, leading to genetic diversity.

Capsule

A form of glycocalyx that consists of a gelatinous layer; found in blue-green algae and certain bacteria.