Unformatted text preview: k . Show that the probability that the last ball is white is the same as the probability that the first ball is white, i.e., it is m / ( m+n ) . Solution: Let W i be the event that a white ball is chosen from the i th jar Starting with the first case, we get g G¹ º ² ¶ » »¼½ . On the other hand, for the second case, g G¹ ¾ ² ¶ g G¹ 2 ¹ 1 ²g G¹ º ² ³ g G¹ 2 ¹ 1 ¿ ²g G¹ 1 ¿ ² g G¹ ¾ ² ¶ À ³ 1 À ³ Á ³ 1 À À ³ Á ³ À À ³ Á ³ 1 Á À ³ Á ¶ À À ³ Á In general, if we continue to find other probabilities, we find g G¹ Â ² ¶ À À³Á ; because it is clear that If g G¹ ÃÄ1 ² ¶ À À ³ Á , then g G¹ Ã ² ¶ À À ³ Á...
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 Spring '11
 memet
 Probability, Probability theory

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