Question

Samples of laboratory glass are in small, light packaging or heavy, large packaging. Suppose that 2% and 1% of the sample shipped in small and large packages, respectively, break during transit. If 58% of the samples are shipped in large packages and 42% are shipped in small packages, what proportion of samples break during shipment

Answer 1

Total proportion of samples that break during shipment
`1.42` %

Explanation:

Let the total number of glasses shipped is equal to
`100`

`58` % of the glasses are shipped in large packets
`(58)/(100)*100 = 58`

`42` % of the glasses are shipped in small packets
`(42)/(100)*100 = 42`

Number of broken glasses in small package
`= (2)/(100) * 42 = 0.84`

Number of broken glasses in large package
`= (1)/(100) * 58 = 0.58`

Total proportion of samples that break during shipment

`(0.84 + 0.58)/(100) *100 = 1.42` %