Question

Two coins are tossed once, where (i) E: tail appears on one coin, F: one coin shows head (ii) E: not tail appears, F: no head appears

Answer 1

It is given that two coins are tossed once.

The sample space S when two coins are tossed once is,

S={ HH,HT,TH,TT }

The total number of sample space is 4.

(i)

Let E be the event of occurring tail on one coin and F be the event of occurring head on one coin.

E={ HT,TH } P( E )= 2 4 = 1 2

And,

F={ HT,TH } P( F )= 2 4 = 1 2

The common occurring between events E and F is,

E∩F={ HT,TH } P( E∩F )= 2 4 = 1 2

The probability P( E|F ) is calculated as,

P( E|F )= P( E∩F ) P( F ) = 2 2 =1

Therefore, the value of P( E|F )is 1.

(ii)

Let E be the event of occurring no tails and F be the event of occurring no heads.

E={ HH } P( E )= 1 4

And,

F={ TT } P( F )= 1 4

The common occurring between events E and F is,

E∩F={ 0 } P( E∩F )=0

The probability P( E|F ) is calculated as,

P( E|F )= P( E∩F ) P( F ) = 0 1 =0

Therefore, the value of P( E|F )is 0.