For the experiment of rolling a single sixsided die once def

For the experiment of rolling a single six-sided die once, define events

T:thenumberrolledisthree

G:thenumberrolledisfourorgreater

A.List the outcomes that comprise T and G.

B.List the outcomes that comprise T G, T G, T^c, and (TG)c.

C.Assuming all outcomes are equally likely, find P(TG), P(TG), and P(Tc).

D.Determine whether or not T and G are mutually exclusive. Explain why or why not.

Solution

a)

T = {3}
G = {4,5,6}

b)

T n G = { } [an empty set, becasue they do not have common elements.

T U G = {3,4,5,6}

Tc = all elements not in T = {1,2,4,5,6}

(T U G)c = all elements not in T U G = {1,2}

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c)

As (T n G) is an empty set,

P(T n G) = 0 [answer]

As T U G has 4 elements out of 6 in the sample space,

P(T U G) = 4/6 = 2/3 = 0.66667 [answer]

P(Tc) = 5/6 = 0.83333 [as it has 5 elements]

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d)

T and G ARE MUTUALLY EXCLUSIVE because their intersection is an empty set. [YES, THEY ARE MUTUALLY EXCLUSIVE]