Question

If two coins are tossed then find the probability of the events.
(i) at least one tail turns up
(ii) no head turns up
(iii) at the most one tail turns up.

Answer 1

Given:
Two coins are tossed.
Sample space = {HH, HT, TH, TT}
Or,
n(S) = 4

(i) Let A be the event of getting at least one tail.
Here,
A = {HT, TH, TT}
∴ n(A) = 3
Thus, we have:
P(A) = $\frac{n\left(\mathrm{A}\right)}{n\left(\mathrm{S}\right)}$
$\Rightarrow$P(A) = $\frac{3}{4}$

(ii) Let B be the event of getting no head.
Here,
B = {TT}
∴ n(B) = 1
Thus, we have:
P(B) = $\frac{n\left(\mathrm{B}\right)}{n\left(\mathrm{S}\right)}$
$\Rightarrow$P(B) =$\frac{1}{4}$

(iii) Let C be the event of getting at most one tail.
Here,
C = {HH, HT, TH}
∴ n(C) = 3
Thus, we have:
P(C) =$\frac{n\left(\mathrm{C}\right)}{n\left(\mathrm{S}\right)}$
$\Rightarrow$P(C) = $\frac{3}{4}$