Question

In a simultaneous toss of two coins, find the probability of getting:
(i) exactly one head,
(ii) atmost one head. ​

Answer 1

${\huge\fbox\pink{♥}\fbox\blue{A}\fbox\purple{N}\fbox\green{S}\fbox\red{W}\fbox\orange{E}\fbox{R}\fbox\gray{♥}}$

The sample space is given by

S = {HH, HT, TH, TT}

Total events n(S) = 4

(i) exactly one head = {HT, TH} = 2

P(exactly one head) = 2/4=1/2

(ii) atmost one head = {HT, TH, TT} = 3

P(atmost one head) = 3/4

Answer 2

$\Large{\bf{Given\::}}$

• Two coins are tossed simultaneously.

$\\ \Large{\bf{To\: Find\::}}$

⑴ Probability of getting exactly one head.

⑵ Probability of getting atmost one head.

$\\ \Large{\bf{Solution\::}}$

☛ When two coins are tossed the outcomes are

✯ {HH, HT, TH, TT} ⠀[H = Head & T = Tail]

Therefore,

➛ Total no. of outcomes = 4

⠀

⑴ Exactly one head

☛ Only two cases that can be possible that are

⠀⠀⠀⠀⠀ ⠀⠀★ {HT, TH} ★

Therefore,

➛ No. of favourable outcomes = 2

$\orange\bigstar\:\mid\:\bf\purple{P(E)\:=\:\dfrac{No.\:of\: favourable\: outcomes}{Total\:no.\:of\: possible\: outcomes}\:}\:\mid\:\green\bigstar$

➟ P(exactly one head) = $\tt{\dfrac{2}{4}\:}$

➟ P(exactly one head) = $\tt\red{\dfrac{1}{2}\:}$

⑵ Atmost one head

☛ There are three cases that can be possible that are

⠀⠀⠀⠀⠀ ⠀★ {HT, TH, TT} ★

Therefore,

➛ No. of favourable outcomes = 3

➳ P(atmost one head) = $\tt\pink{\dfrac{3}{4}\:}$