Spoke Weaving Corporation has eight weaving machines of the

Spoke Weaving Corporation has eight weaving machines of the same kind and of the same age. The probability is 0.06 that any weaving machine will break down at any time.

Round the answers to 4 decimal places.

Find the probability that at any given time

none of the weaving machines will be broken down:

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where     
k = number of successes in trials        
n = is the number of independent trials        
p = probability of success on each trial

P( X = 0 ) = ( 8 0 ) * ( 0.06^0) * ( 1 - 0.06 )^8
= 0.6096