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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

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Answered by bemath last updated on 11/Oct/20

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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