Nikita has three coins. One coin is fair, one coin is biased so that the probability of obtaining a head is $$\(\frac{1}{3}\)$$ and the third coin is biased so that the probability of obtaining a head is $$\(\frac{1}{5}\)$$. The random variable $$\(X\)$$ is the number of heads that Nikita obtains when he throws all three coins at the same time. Use your answer to part (b) to find $$\(\mathrm{E}(Z)\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . * 0000800000012 *

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