A painter has four different jars of paint colors available: red, orange, green,

Question

A painter has four different jars of paint colors available: red, orange, green, and purple. She wants to paint something abstract, so she blindfolds herself, randomly dips her brush, and paints on the canvas. She continues trying paing jars until she finally gets some purple onto the canvas (her assistant will gell her when this happens) and then she stops. Assume that she does not repeat any of the jars because her assistant removes a jar once it has been used.

1.) What is the sample sapce?

A- Purple

B- {R, RP, GP, OP, ROP, RGP, GRP, GOP, ORP, OGP, ROGP}

C- {ROGP}

D- {R, ROGP, RP, GP, RGP}

E- All combos of ROGP that end in P

2.) How many outcomes are in the sample space?

3.) Another painter borrows the 4 jars of paint and performs the same experiment; i.e. selects paints at random, but she allows the jars to be reused (assume there is an unlimited amount of paint in each jar). List a few of the outcomes in the sample space, when repititions are allowed.

A- RGORGORRR

B- RRRGROP

C- RGRGRGPR

4.) Write an expression for the entire sample space for the second painter

A- {P, x_1, x_2, ..... | x_i {R, O, G}}

B- {x_1, x_2, ....., P | x_i {R, O, G}}

C- {R, x_1, x_2, ..... | x_i {R, O, G}}

Explanation / Answer

1) Let the 4 colours red, orange, green, and purple be represented as R,O,G and P. She stops after encountering a purple paint. This could happen in the following ways:

{ P, RP, OP, GP, ROP, RGP, OGP, ORP, GRP, GOP, ROGP, RGOP, GORP, GROP, OGRP, ORGP }

Here basically we have covered all the caes - purple is the first colour encountered, second and so on till fourth.

Therefore E- All combos of ROGP that end in P is the correct answer here.

2) Number of outcomes in the sample space is the number of elements in the set: { P, RP, OP, GP, ROP, RGP, OGP, ORP, GRP, GOP, ROGP, RGOP, GORP, GROP, OGRP, ORGP } that is 16

Therefore 16 is the correct answer here.

3) Now here repetitions are also allowed. So we will check which of the given options are correct

a) RGORGORRR - this is not correct because P is not encountered

b) RRRGROP - this is correct because purple is encountered and at the last

c) RGRGRGPR - this is not correct because P is encountered in between

Therefore b) RRRGROP is the correct answer here.

4) B- {x_1, x_2, ....., P | x_i {R, O, G}} is the correct answer becaise there is no condition on the start of the sample set but it should definitely end with P which is satisfied here.

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