Question

A digital scale that provides weights to the nearest gram is used. Let S denote the entire sample space. Let A denote the event that a weight exceeds 11 grams, let B denote the event that a weight is less than or equal to 15 grams, and let C denote the event that a weight is great than or equal to 8 grams and less than 12 grams. List the elements corresponding to the event A’.

S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000} and E = {1, 3, 5}

Answer 1

a) Elements corresponding to event A:

A = {100, 1000}

Explanation:

From the information provided in the question,

S = {0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000} and S is the sample space. Then;

A = all weights > 11;

B = all weights ≤ 15;

C = ≥ 8 and < 12;

Since sample space (S) consist of all possible events. Then, we have the following:

A = {100, 1000}; since only 100 and 1000 are the only events > 11 within the sample space.

B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; since these are the only events less than or equals to 15 within the sample space.

C = {8, 9, 10}; since these are the only events greater than or equals to 8 and less than 12 within the sample space.

And E = {1, 3, 5} given!