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Question-90258




Question Number 90258 by jagoll last updated on 22/Apr/20
Commented by john santu last updated on 22/Apr/20
(a)P(X≤3) = Σ_(k = 0) ^3 C_k ^(25) (0.05)^k  (0.95)^(3−k)   (b)P(X≥4) = 1−Σ_(k = 0) ^3 C_k ^(25)  (0.05)^k  (0.95)^(3−k)   (c) P(1≤X≤3) = Σ_(k = 1) ^3 C_k ^(25)  (0.05)^k  (0.95)^(3−k)
$$\left({a}\right){P}\left({X}\leqslant\mathrm{3}\right)\:=\:\underset{{k}\:=\:\mathrm{0}} {\overset{\mathrm{3}} {\sum}}{C}_{{k}} ^{\mathrm{25}} \left(\mathrm{0}.\mathrm{05}\right)^{{k}} \:\left(\mathrm{0}.\mathrm{95}\right)^{\mathrm{3}−{k}} \\ $$$$\left({b}\right){P}\left({X}\geqslant\mathrm{4}\right)\:=\:\mathrm{1}−\underset{{k}\:=\:\mathrm{0}} {\overset{\mathrm{3}} {\sum}}{C}_{{k}} ^{\mathrm{25}} \:\left(\mathrm{0}.\mathrm{05}\right)^{{k}} \:\left(\mathrm{0}.\mathrm{95}\right)^{\mathrm{3}−{k}} \\ $$$$\left({c}\right)\:{P}\left(\mathrm{1}\leqslant{X}\leqslant\mathrm{3}\right)\:=\:\underset{{k}\:=\:\mathrm{1}} {\overset{\mathrm{3}} {\sum}}{C}_{{k}} ^{\mathrm{25}} \:\left(\mathrm{0}.\mathrm{05}\right)^{{k}} \:\left(\mathrm{0}.\mathrm{95}\right)^{\mathrm{3}−{k}} \\ $$

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