$A die is rolled . Let us define event E_{1} as the set of possible outcomes where the number on the face of the die is even and event E_{2} as the set of possible outcomes where the number on the face of the die is odd . Event E_{1} and E_{2} are mutually exclusive .$

True

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False

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Solution

The correct option is A True

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If $E_{1}, E_{2}, E_{3} \dots E_{n}$ are n events of a sample space S and if $E_{1} \cup E_{2} \cup E_{3} \cup \dots E_{n} = S$ , then $E_{1}, E_{2} \dots E_{n}$ are called mutually exclusive and exhaustive events.

Let two fair six - faced dice A and B be thrown simultaneously. If $E_{1}$ is the event that die A shows up four, $E_{2}$ is the event that die B shows up two and $E_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?