A painter has four different jars of paint colors available, exactly one of whic

Question

A painter has four different jars of paint colors available, exactly one of which is purple. She wants to paint something abstract, so she blindfolds herself, randomly dips her brush, and paints on the canvas. She continues trying paint jars until she finally gets some purple onto the canvas (her assistant will tell her when this happens). Assume that she does not repeat any of the jars because her assistant removes a jar once it has been used. How many outcomes are in the sample space? What are they? Another painter borrows the four jars of paint and performs the same experiment; i e., selects paint at random; but she allows the jars to be reused, perhaps over and over many times (assume each contains an unlimited amount of paint). List a few of the outcomes in the sample space, when repetitions are allowed.

Explanation / Answer

let A, B.C, D are 4 Jars, out of which D contains purple

a) as she finished with purple,

purple can be 1st , 2nd , 3rd or 4th choice.

if purple is 1st choice , number of outcome =1 and that is D

if 2nd ; number of outcome =3 ; as first one has 3 choices.and they are AD, BD, CD

if 3rd , number of outcome 3*2 =6 ; as first one has3 choices and second has 2. outcomes are ABD, ACD,BCD,BAD,CAD,CBD

if 4th , number of outcome =3*2*1=6, ABCD, ACBD.BCAD,BACD,CABD,CBAD

hence total 16 outcomes.

c) if repetition is allowed there can be infinite outcomes.

like AABCABD, BCAD, D, CCABCACBCCBAAACCD etc.

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