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

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Solution

In the given experiment, a die is rolled.

Let, E be the event “the die shows 4”.So set E contains the element 4.

E={ 4 }

Let, F be the event that die shows even number”. So set F contains all the even numbers from 1 to 6.

F={ 2,4,6 }

Two events, A and B are mutually exclusive if, A∩B=ϕ.

E∩F={ 4 }∩{ 2,4,6 } =4 .

It can be observed that E∩F≠ϕ.

Thus, E and F are not mutually exclusive.

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Similar questions

E

4

F

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 .

Two dice are thrown. The events A, B, C, D, E and F are described as follows :

A = Getting an even number on the first die.

B = Getting an odd number on the first die.

C = Getting at most 5 as sum of the numbers on the two dice.

D = Getting the sum of the numbers on the dice greater than 5 but less than 10.

E = Getting at least 10 as the sum of the numbers on the dice.

F = Getting an odd number on one of the dice.

(i) Describe the following events : A and B, B or C, B and C, A and E, A or F, A and F

(ii) State true or false :

(a) A and B are mutually exclusive.

(b) A and B are mutually exclusive and exhaustive events.

(d) C and D are mutually exclusive and exhaustive events.

(e) C, D and E are mutually exclusive and exhaustive events.

(f) A' and B' are mutually exclusive events.

(g) A, B, F arc mutually exclusive and exhaustive events.

E = {1, 3, 5}

F = {2, 3}

P (E | F)

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