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# Quiz1_friday_answers - k Show that the probability that the...

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Theory of Probability – Friday Section 11.03.2011 Quiz-1 1. Mary, a university student, has a basket that contains 5 blue socks, 4 red socks and 2 green socks. In the dark, she picks two socks at random from the basket. What is the probability that both socks are the same color? Solution: Let B : The event that the two socks are both blue R : The event that the two socks are both red G : The event that the two socks are both green. g G±² ³ g G´² ³ g Gµ² ¶ · 5 2 ¸ · 11 2 ¸ ³ · 4 2 ¸ · 11 2 ¸ ³ · 2 2 ¸ · 11 2 ¸ 17 55 2. Each of k jars contains m white and n black balls. A ball is randomly chosen from jar 1 and transferred to jar 2, and then a ball is randomly chosen from jar 2 and transferred to jar 3, etc. Finally, a ball is randomly chosen from jar
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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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