Math

QuestionSelect a letter from A to G. Find outcomes for these events: (a) Event "X and Y": (b) Event "X or Y": (c) The complement of event X.

Studdy Solution

STEP 1

Assumptions1. The tiles are labeled with the first seven letters of the alphabet a, b, c, d, e, f, g. . Event X is defined as the letter selected being found in the word "BAG".
3. Event Y is defined as the letter selected comes after "C" in the alphabet.
4. Event X and Y means the letter selected must satisfy both conditions of X and Y.
5. Event X or Y means the letter selected can satisfy either condition of X or Y.
6. The complement of an event is the set of outcomes that are not in the event.

STEP 2

First, we need to determine the outcomes for event X. This is the set of letters that are found in the word "BAG".
X={b,a,g}X = \{b, a, g\}

STEP 3

Next, we need to determine the outcomes for event Y. This is the set of letters that come after "C" in the alphabet.
Y={d,e,f,g}Y = \{d, e, f, g\}

STEP 4

Now, we can find the intersection of events X and Y. This is the set of letters that satisfy both conditions of X and Y.
XY={b,a,g}{d,e,f,g}X \cap Y = \{b, a, g\} \cap \{d, e, f, g\}

STEP 5

Calculate the intersection of X and Y.
XY={g}X \cap Y = \{g\}So, the outcome for event "X and Y" is g.

STEP 6

Next, we can find the union of events X and Y. This is the set of letters that satisfy either condition of X or Y.
XY={b,a,g}{d,e,f,g}X \cup Y = \{b, a, g\} \cup \{d, e, f, g\}

STEP 7

Calculate the union of X and Y.
XY={a,b,d,e,f,g}X \cup Y = \{a, b, d, e, f, g\}So, the outcome for event "X or Y" is a, b, d, e, f, g.

STEP 8

Finally, we can find the complement of event X. This is the set of letters that are not in event X.
X={a,b,c,d,e,f,g}{b,a,g}X' = \{a, b, c, d, e, f, g\} - \{b, a, g\}

STEP 9

Calculate the complement of X.
X={c,d,e,f}X' = \{c, d, e, f\}So, the outcome for the complement of event X is c, d, e, f.

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