If 20% of the bolts produced by a machine are defective, determine the probability that out of 4 bolts chosen at random (a) 1,(b)0,(c) less than 2 , bolts will be defective.
The probability of a defective bolt is p=0.2, of a nondefective bolt is q=1−p=0.8. Let the random variable X be the number of defective bolts. Then
P(x=1)=( 4 1 ) (0,2)¹ (0, 8)³=0.4096