Question

iii), Three coins are tossed simultaneously. Find the probability
of the following events :
(a) Event A : No head appears (b) Event B: Head appears
at least twice (c) Event C: Head appears twice.​

Answer 1

Given : ↴

$\sf \: Three \: coins \: are \: tossed \: simultaneously.$

To find : ↴

$\sf \: We \: have \: to \: find \: the \: probobility \: of \: the \: following \: events \: :$

$\sf \: (a) \: Event \: A \: : \: No \: \: head \: appears.$

$\sf \: (b) \: Event \: B \: : \: Head \: appears$

$\sf \: (c) \: Event \: C \: : \: Head \: appears \: twice.$

So, Let's do it : ↴

$\sf \: When \: three \: coins \: are \: tossed \: simultaneously \: ..$

$\sf \: Then \: the \: Sample \: Space \: (S) \: is \: : \:$ ↴

$\fbox\pink{HHH, HTT, HTH, HHT, TTT, THH, THT, TTH}$

$\sf \: \longmapsto \: Total \: number \: of \: Outcomes \: = \: 8.$

$\sf \: Formula \: to \: Find \: the \: Probobility \: is \: :$ ↴

$\sf \boxed { \sf \: \dfrac{No. \: of \: Favourable \: outcomes }{Total \: no. \: of \: Outcomes } }$

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$\sf \: (a) \: Event \: A \: : \: No \: \: head \: appears.$

$\sf \: \longrightarrow \: Favourable \: outcomes \: = 1$

$\sf \longrightarrow \: Total \: Outcome \: = \: 8$

$\boxed{ \sf \: P \: ( Getting \: No \: head) = \: \dfrac{1}{8} }$

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$\sf \: (b) \: Event \: B \: : \: Head \: appears$

$\sf \: \longrightarrow \: Favourable \: outcomes \: = 7$

$\sf \longrightarrow \: Total \: Outcome \: = \: 8$

$\boxed{ \sf \: P \: ( Getting \: Head) = \: \dfrac{7}{8} }$

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$\sf \: (c) \: Event \: C \: : \: Head \: appears \: twice.$

$\sf \: \longrightarrow \: Favourable \: outcomes \: = 3$

$\sf \longrightarrow \: Total \: Outcome \: = \: 8$

$\boxed{ \sf \: P \: (Getting \: Head \: 2\: times) = \: \dfrac{3}{8} }$