Practice WorkSheet For Marble Problem

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1. There are 5 Blue, 6 Green, and 10 Red marbles. If two marbles are drawn Find the following;

A) The Sample Space for the experiment.

Solution:

Let B=Blue, G=Green, R=Red
{(2R, 2B, 2G, 1R1B, 1R1G, 1B1G)}




B) Find the Probability that both marbles are Blue.
(Do NOT use the compliment).

Solution:
P(Both Blue) =C(5,2)/C(21,2)=.048



C) Find the Probability that both marbles are Blue using the compliment.

Solution:
P(Both Blue) = 1 - P(Not both blue)

=1 - [P(2 G)+P(2 R)+(1B & 1 G)+P(1 B & 1 R)+P(1 G & 1 R)]

= 1 - [(C(6,2)+C(10,2)+C(5,1)C(6,1)+C(5,1)C(10,1)+C(6,1)C(10,1))/C(21,2)]

= 1 - [(15+45+30+50+60)/210]

= 1 - [200/210] = .048

Answers will be below for the following. Work them out then check yourself.



D) Find the Probability of drawing two marbles in which neither is Red.
(Do NOT use the compliment).



E) Find the Probability of drawing two marbles in which neither is Red.
( Use the compliment)



F) Find the Probability of drawing two marbles in which the marbles are different colors. (Do NOT use the compliment).



G) Find the Probability of drawing two marbles in which the marbles are different colors. (Use the compliment).



******************ANSWERS********************

1d)   P(neither Red) = P(Both B) + P(Both G)+P(1 B & 1 G)

= [C(5,2) + C(6,2) + C(5,1)C(6,1)]/C(21,2)

= (10+15+30)/210

= .26



1e)   P(neither Red) = 1 - [P(all others in sample space which have red)

S={(2 B), (2 G), (2 R), (1B & 1 G), (1B & 1 R), (1 G & 1 R)}

= 1 - [P(2 R) + P(1 B & 1 R) + P(1 G & 1 R)]

= 1 - [(C(10,2) + C(5,1)C(10,1)+ C(6,1)C(10,1))/C(21,2)]

= 1 - [(45+50+60)/210]

= .26



1f)   P(Different Colors)=P(1 B & 1 G)+P(1B & 1R) +P(1G & 1 R)

= (30 + 50 +60)/210

= .67



1g)   P(Different Colors)=1 - [P(Not different Colors)]

= 1 - [P(2B) +P(2G) + P(2R)]

= 1 - [(10 + 15 + 45)/210]

= .67