A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the number obtained is less than $$5.$$ Then $$P\left( {A \cup B} \right)$$ is :
JEE · Math · previous-year question
- A.$${3 \over 5}$$
- B.$$0$$
- C.$$1$$correct
- D.$${2 \over 5}$$
Answer
C. $$1$$
Explanation
No of outcome for a die = { 1, 2, 3, 4, 5, 6 } According to the question, A = { 4, 5, 6 } $$\therefore$$ P(A) = $${3 \over 6}$$ B = { 1, 2, 3, 4 } $$\therefore$$ P(A) = $${4 \over 6}$$ A $$ \cap $$ B = { 4 } So P(A $$ \cap $$ B) = $${1 \over 6}$$ We know, $$P\left( {A \cup B} \right)$$ = $$P\left( A \right)$$ + $$P\left( B \right)$$ - $$P\left( {A \cap B} \right)$$ $$\therefore$$ $$P\left( {A \cup B} \right)$$ = $${3 \over 6}$$ + $${4 \over 6}$$ - $${1 \over 6}$$ = $${{7 - 1} \over 6}$$ = $${6 \over 6}$$ = 1 $$\therefore$$ Option (C) is correct.
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