PROBABILITY — MATHS STD 11 Science — Question

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Now, let A be the event: getting at least two heads = {HHH, HHT, HTH, THH}
B be the event: getting exactly one head = {HTT, THT, TTH}
and C be th event: getting no head = {TTT}

Mutually exclusive events are those in which no element is common
Since ${A\cap B=\phi}$. $\therefore$ A and B are mutually exclusive events,
$\style{font-size:28px}{B\cap C=\phi}$. $\therefore$ B and C are mutually exclusive events,
$\style{font-size:28px}{A\cap C=\phi}$. $\therefore$ A and C are mutually exclusive events.
Thus A, B, C are mutually exclusive events.
Also, as ${A\cup B\cup C=\{HHH,\;HHT,\;HTH,\;THH,\;HTT,\;THT,\;TTH,\;TTT\}=S}$
So, A, B, C are exhaustive events.
A, B, C are three events which are mutually exclusive and exhaustive.