A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.
The letter selected will be recorded as the outcome.
Consider the following events.
Event : The letter selected comes before " .
Event : The letter selected is found in the word “FACE”.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event " or
(b) Event " and
© The complement of the event

Ask by Bob Bright. in the United States

Mar 28,2025

Question

A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet.
The letter selected will be recorded as the outcome.
Consider the following events.
Event : The letter selected comes before " .
Event : The letter selected is found in the word “FACE”.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event " or
(b) Event " and
© The complement of the event

Ask by Bob Bright. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

(a) We have
$$
X = \{A, B, C, D\} \quad \text{and} \quad Y = \{F, A, C, E\}.
$$
The complement of $$ Y $$ is
$$
Y^{n} = \text{Sample Space} - Y = \{B, D, G\}.
$$
Thus, the event $$ X \text{ or } Y^{n} $$ is the union:
$$
X \cup Y^{n} = \{A, B, C, D\} \cup \{B, D, G\} = \{A, B, C, D, G\}.
$$

(b) The event $$ X \text{ and } Y^{n} $$ is the intersection:
$$
X \cap Y^{n} = \{A, B, C, D\} \cap \{B, D, G\} = \{B, D\}.
$$

(c) The complement of $$ X $$ is all letters not in $$ X $$:
$$
X^{c} = \{A, B, C, D, E, F, G\} - \{A, B, C, D\} = \{E, F, G\}.
$$
(a) $$ X \text{ or } Y^{n} = A, B, C, D, G $$ (b) $$ X \text{ and } Y^{n} = B, D $$ (c) Complement of $$ X = E, F, G $$

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