Question

An aluminum bracket is assembled onto the wing spar of a commercial aircraft using 100 bolts. The bolts have a specification for torque. Assume 5 bolts are not torqued to the proper limit.
Three (3) bolts are selected at random to be checked for the torque specification. ANY BOLT IS ONLY CHOSEN ONCE (this is sampling WITHOUT REPLACEMENT)

What is the probability that the third bolt selected is NOT torqued to specification?
What is the probability that the third bolt selected IS torqued to specification?

Answer 1

Number of bolts torqued to specification = 95

Number of bolts not torqued to specification = 5

Total number of bolts = 100

P(the third bolt selected is not torqued to specification) = P(a bolt being not torqued to specification)

= 5/100 (irrespective of the position, the probability remains same unless any other condition is mentioned)

= 0.05

P(the third bolt selected is torqued to specification) = 1 - P(the third bolt selected is not torqued to specification)

= 1 - 0.05

= 0.95