Question

Two coins are tossed simultaneously. Find the probability of getting
i) at least one head
ii) at most one head
iii) exactly two heads
iv) exactly one head
v) no head
vi) no tail
vii) at least one tail
viii) at most one tail
ix) exactly two tails
x) exactly one tail
xi) almost two tails

Answer 1

Sample Space when two coins are tossed :-

{(H,H), (H,T), (T,T), (T,H)}

(i) p(getting at least one head) = 3/4

= (H,H), (H,T), (T,H)

(ii) p(getting at most one head) = 2/4 = 1/2

= (H,T),(T,H)

(iii) p(getting exactly two heads) = 1/4

= (H,H)

(iv) p(getting exactly one head) = 2/4 = 1/2

= (H,T), (T,H)

(v) p(getting no head) = 1/4

= (T,T)

(vi) p(getting no tail) = 1/4

= (H,H)

(vii) p(getting at least one tail) = 3/4

= (H,T), (T,T), (T,H)

(viii) p(getting at most one tail) = 2/4 = 1/2

= (H,T), (T,H)

(ix) p(getting exactly two tails) = 1/4

= (T,T)

(x) p(getting exactly one tail) = 2/4 = 1/2

= (H,T), (T,H)

(xi) p(getting at most two tails) = 3/4

= (H,T), (T,T), (T,H)

Answer 2

|| ✯✯ QUESTION ✯✯ ||

Two coins are tossed simultaneously. Find the probability of getting : -

i) At least one head

ii) At most one head

iii) Exactly two heads

iv) Exactly one head

v) No head

vi) No tail

vii) At least one tail

viii) At most one tail

ix) Exactly two tails

x) Exactly one tail

xi) Almost two tails.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

✰✰ ANSWER ✰✰

$Total\:Outcomes = 4 (HH , TT ,HT ,TH)</p><p>[tex]\large{\boxed{\bold{\bold{\pink{\sf{(i)At\:least\:One\:Head}}}}}}$

$⇝Outcomes = 3 ( HH , HT , TH )$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$\dfrac{3}{4}$

$\large{\boxed{\bold{\bold{\red{\sf{(ii)At\:Most\:One\:Head}}}}}}$

$⇝Outcomes=2 (HT , TH)$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability=\cancel\dfrac{2}{4}⟹\dfrac{1}{2}$

$\large{\boxed{\bold{\bold{\purple{\sf{(iii)Exactly\:Two\:Heads:}}}}}}$

$⇝Outcomes=1 (HH)$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability=\dfrac{1}{4}$

$\large{\boxed{\bold{\bold{\green{\sf{(iv)Exactly\:One\:Head:}}}}}}$

$⇝Outcomes=2 (HT ,TH)$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability=\cancel\dfrac{2}{4}⟹\dfrac{1}{2}$

$\large{\boxed{\bold{\bold{\blue{\sf{(v)No\:Head:}}}}}}$

$⇝Outcomes=1 (TT)$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability=\dfrac{1}{4}$

$\large{\boxed{\bold{\bold{\orange{\sf{(vi)No\:Tail:}}}}}}$

$⇝Outcomes=1 (HH)$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability = \dfrac{1}{4}$

$\large{\boxed{\bold{\bold{\green{\sf{(vii)At\:Least\:One\:Tail:}}}}}}$

$⇝Outcomes=3 (TT , HT ,TH )$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability = \dfrac{3}{4}$

$\large{\boxed{\bold{\bold{\pink{\sf{(viii)At\:Most\:One\:Tail:}}}}}}$

$⇝Outcomes=2 (HT , TH )</p><p></p><p>[tex]⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability=\cancel\dfrac{2}{4}⟹\dfrac{1}{2}$

$\large{\boxed{\bold{\bold{\red{\sf{(ix)Exactly\:Two\:Tails:}}}}}}$

$⇝Outcomes = 1 (TT)$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability=\dfrac{1}{4}$

$\large{\boxed{\bold{\bold{\orange{\sf{(x)Exactly\:one\:Tail:}}}}}}$

$⇝Outcomes = 2(HT ,TH )$

$⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability =\cancel\dfrac{2}{4}⟹\dfrac{1}{2}$

$\large{\boxed{\bold{\bold{\blue{\sf{(xi)Almost\:Two\:Tails:}}}}}}$

$⇝Outcomes=3 (HT,TH,TT)</p><p></p><p>[tex]⇝Probability = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability = \dfrac{3}{4}$

_____________________

Here :.

H = Head

T= Tail

_____________________