# Sets

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In control replication, cells are replicated over a period of two days. Not until mitosis is completed, can freshly-synthesized DNA be replicated again. Two control mechanisms have been identified - one positive and one negative. Suppose that a replication is observed in three cells.

Let A denote the event that all cells are positive and B denote the event that all cells are negative.

Describe the sample space. Describe the following:

(a) A

(b) B

(c) the intersection of A and B

(d) the union of A and B

https://brainmass.com/statistics/sampling/sample-spaces-sets-union-intersections-204076

#### Solution Preview

Call a positive mechanism P and a negative mechanism N. There are 3 cells, and each cell can use a positive or negative mechanism (so, it can be represented as P or N). The sample space is the list of all of the possible outcomes of the 3 cells. The sample space looks like:

PPP

PPN

PNP

PNN

NPP

NPN

NNP

NNN

a) A is the event that all cells are positive. A consists of only one of the eight possible outcomes in the sample space.

A = {PPP}.

b) B is the event that all cells are ...

#### Solution Summary

The expert examines sample spaces and sets for unions and intersections.