•There are two colored marbles and one white marble in a box. Gwen mixes the marbles,...
•There are two colored marbles and one white marble in a box. Gwen mixes the marbles, and Arthur draws two marbles at random without replacement. If the two marbles match, Arthur wins; otherwise, Gwen wins. Does each player have an equal chance of winning?
Homework Answers
Arthur takes out two marbles without replacement here. Note that there are only 3 marbles here out of which 2 are drawn. Arthur could only win if both the coloured marbles and taken out, otherwise Gwen wins.
The probability of Arthur winning is computed here as:
= Number of ways to select 2 coloured marbles form 2 coloured
marbles / Total number of ways to select 2 marbles from 3
marbles
Therefore P(arthur wins) = 1/3 and thus P(Gwen wins) = 2/3
Therefore they clearly dont have an equal chance of winning.
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