Question

$\left(a\right)$ Two unbiased coins are tossed simultaneously. Find the probability of getting
$\left(i\right)$ Exactly one head
$\left(ii\right)$ Exactly one tail
$\left(iii\right)$ Two tails
$\left(iv\right)$ Atleast one tail
$\left(v\right)$ Atmost one tail
$\left(vi\right)$ No Tail
$\left(b\right)$ Harpreet tossed two different coins simultaneously. What is the probability that she gets at least one head?

Answer 1

Here S=(HH,HT,TH,TT)
(i) Exactly one head
Let A=event of getting one head (HT,TT)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{2}{4}=\frac{1}{2}$

(ii) Exactly one tail
Let A=event of getting one head tail (HT,TH)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{2}{4}=\frac{1}{2}$

(iii) Two tails
Let A=event of getting two tail (,TT)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{1}{4}$

(iv) Atleast one tail
LET A=event of getting atleast one tail (HT,TH,TT)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{3}{4}$

(v) Atmost one tail
Let event of getting Atmost one tail (HT,TH,TT)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{3}{4}$

(vi) No Tail
Let event of getting No Tail (HH)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{1}{4}$

(b)Gets at least one head
Here S=(HH,HT,TH,TT)
Let event of at least one head(HT,TH,TT)
P(A)=$\frac{N\left(A\right)}{N\left(S\right)}=\frac{3}{4}$