Given info:

There are 2% and 1% of the sample shipped in small and large packages, respectively, break during transit. If 60% of the samples are shipped in large packages and 40% are shipped in small packages.

Calculation:

Total probability rule for two events:

For any events A and B, the probability of A is,

P(A)=P(A∩B)+P(A∩B′)=P(A|B)P(B)+P(A|B′)P(B′)

Let B denote the event that a glass breaks.

      L denote the event that large packaging is used.

From given information, P(B|L)=0.01,P(L)=0.60 and P(B|L′)=0.02

The formula for finding the proportion of samples break during shipment is,

P(B)=P(B|L)P(L)+P(B|L′)P(L′)=P(B|L)P(L)+P(B|L′)(1−P(L))

That is,

P(D|L)=(0.01)(0.60)+(0.02)(0.40)=0.006+0.008=0.014

Thus, the proportion of samples break during shipment is 0.014.