Answer:
a) 1.4% of the samples break during shipment
b) the probability is 4/7 ( 57.14%)
Step-by-step explanation:
a) defining the event B= the sample of laboratory glass breaks , then the probability is:
P(B)= probability that sample is shipped in small packaging * probability that the sample breaks given that was shipped in small packaging + probability that sample is shipped in large packaging * probability that the sample breaks given that was shipped in large packaging = 0.40* 0.02 + 0.60*0.01 = 0.014
b) we can use the theorem of Bayes for conditional probability. Then defining the event S= the sample is shipped in small packaging . Thus we have
P(S/B)= P(S∩B)/P(B) = 0.40* 0.02 / 0.014= 4/7 ( 57.14%)
where
P(S∩B)= probability that sample is shipped in small packaging and it breaks
P(S/B)= probability that sample was shipped in small packaging given that is broken
