Question

Measurements of the thickness of a part are modeled with the sample space: S = R+.

Let  , E1 = (10 ≤ x <13)

Let E2 = (12 ≤ x < 16)

Then (E1'⋂E2)

Answer 1

We are given the sample space here as: R+ which means set of all positive real numbers.

Also, we are given here the definitions of E1 and E2 as:
E1 = { 10 <= x < 13 }
E2 = { 12 <= x < 16 }
Therefore, E1' is the complement of E1 which is given here as:
E1' = not E1 = { 0 < x < 10 or x >= 13 }
E2 = { 12 <= x < 16 }

Therefore, E1'⋂E2 is given as set of outcomes which are both in E1' and E2.

Therefore,
E1' ⋂E2 = { 13 <= x < 16 }

Therefore { 13 <= x < 16 } is the required set of outcomes here.