2. Total probability problem. Heavy-large packaging. Suppose that 2% and 1% of t

Question

2. Total probability problem. Heavy-large packaging. Suppose that 2% and 1% of the glass samples and Samples of laboratory glass are in small-light packaging or samples large packages shipped in small and large packages, respectively, breaks during transit. If 60% of the glass is shipped in 40% are shipped in small packages: What proportion of glass samples breaks during transit? 2. Total probability problem. Heavy-large packaging. Suppose that 2% and 1% of the glass samples and Samples of laboratory glass are in small-light packaging or samples large packages shipped in small and large packages, respectively, breaks during transit. If 60% of the glass is shipped in 40% are shipped in small packages: What proportion of glass samples breaks during transit?

Explanation / Answer

2% of glass samples in small packages breaks. 40% are shipped in small packages.

1% of glass samples in large packages breaks. 60% are shipped in large packages.

Therefore we are given that:

P( break | Small ) = 0.02 , P(Small) = 0.4

P( break | Large ) = 0.01 , P(Large) = 0.6

Therefore by the use of law of total probability we get:

P(Break ) = P(Break | Small )P(Small ) + P( Break | Large )P(Large ) = 0.02*0.4 + 0.01*0.6 = 0.008 + 0.006 = 0.014

Therefore the proportion of glass samples which breaks during the transit would be 0.014

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