A gambler plays a sequence of games that she either wins or

A gambler plays a sequence of games that she either wins or loses. The outcomes of the games are independent, and the probability that the gambler wins is 60%. The gambler stops playing as soon as she either has won a total of 2 games or has lost a total of 3 games. Let T be the number of games played by the gambler. a) Draw a tree diagram to illustrate this situation. b) What values can T take? c) Make a table of the probabilities associated with each value of T. d) Find the mean of T. e) Find the standard deviation of T.

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