A die is rolled. Let E be the event “die shows 4” and F be the event “die shows an even number”. Are E and F multually exclusive?

Solution

A die is rolled.
∴ the sample space, S = {1, 2, 3, ,4, 5, 6}
Event E: the die shows 4
$rightwards double arrow$ E = {4}
Event F: the die shows an even number
$rightwards double arrow$ F = {2, 4, 6}
Now, $straight E intersection straight F space equals space left curly bracket 4 right curly bracket space intersection space left curly bracket 2 comma space 4 comma space 6 right curly bracket space equals space left curly bracket 4 right curly bracket space not equal to space straight ϕ$
Hence, E and F are not mutually exclusive.

Some More Questions From Straight Lines Chapter

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in the number of girls in the family?

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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Straight Lines

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows an even number”. Are E and F multually exclusive?

Some More Questions From Straight Lines Chapter

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in the number of girls in the family?

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

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