a coin tossed 8 times. Probability of appearing head at least 3 times is _


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Question Number 117339 by john santu last updated on 11/Oct/20

$a c o i n t o s s e d 8 t i m e s . P r o b a b i l i t y$ $o f a p p e a r i n g h e a d a t l e a s t 3 t i m e s i s$ $__$
	Answered by bemath last updated on 11/Oct/20
	$by Binomial distribution we have p=(1/2) , n = 8 , X≥3 p(X≥3) = Σ_(n=3) ^8 b(x,8,(1/2)) = 1−{p(X=0)+p(X=1)+p(X=2)} =1−{C_0 ^8 ((1/2))^8 +C_1 ^8 ((1/2))^8 +C_2 ^8 ((1/2))^8 } =1−{(1/(256))+(8/(256))+((28)/(256))} =1−((37)/(256)) = 0.855469$
	$by Binomial distribution$ $we have p = \frac{1}{2}, n = 8, X ⩾ 3$ $p (X ⩾ 3) = \underset{n = 3}{\sum^{8}} b (x, 8, \frac{1}{2})$ $= 1 - {p (X = 0) + p (X = 1) + p (X = 2)}$ $= 1 - {C_{0}^{8} {(\frac{1}{2})}^{8} + C_{1}^{8} {(\frac{1}{2})}^{8} + C_{2}^{8} {(\frac{1}{2})}^{8}}$ $= 1 - {\frac{1}{256} + \frac{8}{256} + \frac{28}{256}}$ $= 1 - \frac{37}{256} = 0.855469$
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