Compute the Following Binomial Probabilities Directly from the Formula for B(x;n,p)

Question

Examlex · Accepted Answer

The Answer is a.

b ( 3 ; 8,7 ) = \left( \begin{array} { l } 8 \3\end{array} ight) ( .7 ) ^ { 3 } ( .3 ) ^ { 5 } = ( 56 ) ( .00083349 ) = .0467

b.

b ( 5 ; 8,7 ) = \left( \begin{array} { l } 8 \5\end{array} ight) ( .7 ) ^ { 5 } ( .3 ) ^ { 3 } = ( 56 ) ( .00453789 ) = .2541

c.

P ( 3 \leq X \leq 5 ) = b ( 3 ; 8,6 ) + b ( 4 ; 8,6 ) + b ( 5 ; 8,6 ) = .0467 + .1361 + .2541 = .4369

d.

P ( X \geq 1 ) = 1 - P ( X = 0 ) = 1 - \left( \begin{array} { l } 10 \0\end{array} ight) ( .1 ) ^ { 10 } ( .9 ) ^ { 10 } = 1 - ( .9 ) ^ { 10 } = .6513

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