Question

1. An experiment consists of drawing balls from an urn which contains 2 red balls, one white ball, and one

blue ball. The balls are drawn, without replacement, until either a blue ball has been drawn or two different

colors have been drawn. If an outcome of this experiment consists of an ordered list of the colors of the

balls drawn, how may outcomes exist?

2. An experiment consists of repeatedly drawing a ball from an urn which contains 3 red balls and 5 blue balls. After each drawing, the color of the ball is noted and that ball is discarded. The experiment continues until two consecutive red balls are drawn or two consecutive blue balls are drawn. If an outcome consists of an ordered list of the colors of the balls drawn, how many outcomes exist?

3. An experiment consists of measuring widgets, one after another, and classifying them as long, short, or O.K. The experiment ends when either one short widget, two long widgets, or a total of three widgets have been measured. How many outcomes are in the sample space of this experiment?

Answer 1

1.

Let R, B, W denote the outcomes of red, blue and white balls respectively.

The possible outcomes are,

{B}

{RB}

{WB}

{RRB}

{WR}

{RW}

{RRW}

Number of outcomes is 7.

2.

Let R, B denote the outcomes of red and blue balls respectively.

{RR}

{RBRR}

{RBB}

{RBRBRBB}

{RBRBB}

{BB}

{BRBB}

{BRR}

{BRBRBB}

{BRBRR}

{BRBRBRBB}

Number of outcomes is 11.

3.

Let L, S, O denote the outcomes of long, shot and OK widgets respectively.

The possible outcomes are,

{S}

{LS}

{LL}

{LOS}

{LOL}

{LOO}

{OS}

{OLS}

{OLL}

{OLO}

{OOS}

{OOL}

{OOO}

Number of outcomes is 13.