Three coins are tossed once. Let A denote the | vedclass

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Question

When three coins are tossed, the sample space is given by

$S =\{ HHH ,\, HHT , \,HTH ,\, HTT , \,THH ,\, THT , \,TTH ,&nbs

Vedclass · Accepted Answer

Vedclass · Answer

When three coins are tossed, the sample space is given by

$S =\{ HHH ,\, HHT , \,HTH ,\, HTT , \,THH ,\, THT , \,TTH , \,TTT \}$

Accordingly,

$A=\{H H H\}$

$B =\{ HHT ,\, HTH ,\, THH \}$

$C =\{ TTT \}$

$D =\{ HHH , \,HHT , \,HTH , \,HTT \}$

We now observe that

$A \cap B$ $=\phi, A \cap C$ $=\phi, A \cap D$ $=\{H H H\} 
eq \phi$

$B \cap C=\phi, B \cap D$ $=\{H H T,\, H T H\} 
eq \phi$

$C \cap D=\phi$

If an event has only one sample point of a sample space, it is called a simple event. Thus, $A$ and $C$ are simple events.

Three coins are tossed once. Let $A$ denote the event ' three heads show ', $B$ denote the event ' two heads and one tail show ' , $C$ denote the event ' three tails show and $D$ denote the event 'a head shows on the first coin '. Which events are simple ?

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