Question

A die is thrown. Describe the following events: (i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3 (iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3 Also find

Answer 1

In the given experiment, a die is thrown.

(i)

The event is, A: a number less than 7.

A={ 1,2,3,4,5,6 }.

(ii)

The event is, B: a number is greater than 7.

B={ ϕ }

(iii)

The event is, C: a number is multiple of 3.

C={ 3,6 }

(iv)

The event is, D: a number isless than 4.

D={ 1,2,3 }

(v)

The event is, E: aneven number greater than 4.

E={ 6 }

(vi)

The event is, F: a number is not less than 3.

F={ 3,4,5,6 }

Now,

A∪B=( { 1,2,3,4,5,6 }∪{ ϕ } ) ={ 1,2,3,4,5,6 }

A∩B=( { 1,2,3,4,5,6 }∩{ ϕ } ) ={ ϕ }

B∪C=( { ϕ }∪{ 3,6 } ) ={ 3,6 }

E∩F=( { 6 }∩{ 3,4,5,6 } ) ={ 6 }

D∩E=( { 1,2,3 }∩{ 6 } ) ={ ϕ }

E∩F=( { 6 }∩{ 3,4,5,6 } ) ={ 6 }

A−C=( { 1,2,3,4,5,6 }−{ 3,6 } ) ={ 1,2,4,5 }

D−E=( { 1,2,3 }−{ 6 } ) ={ 1,2,3 }

F ′ ={ 1,2 }

E∩ F ′ =( { 6 }∩{ 1,2 } ) ={ ϕ }