Question

During 1 hour, a machine use 12 minutes to produce component A and 48 minutes to produce component B, the breakdown rate when producing component A is 0.3 and the breakdown rate when producing component B is 0.4. What is the probability that this machine would break down within one-hour producing session?

Answer 1

Probability that component A is produced within 1-hour period = P(A) = 12/60 = 0.2

Probability that component B is produced within 1-hour period = P(B) = 48/60 = 0.8

Probability that machine breaks while producing component A = P(breakdown | A) = 0.3

Probability that machine breaks while producing component B =  P(breakdown | B) = 0.4

By law of total probability,

probability that this machine would break down within one-hour producing session = P(breakdown)

= P(breakdown | A) P(A) + P(breakdown | B) P(B)

= 0.3 * 0.2 + 0.4 * 0.8

= 0.38