Question

If two coins are tossed, find the probability of the following events.
(1) Getting at least one head.
(2) Getting no head.

Answer 1

Sample Space (S) = {HH, HT, TT, TH}
∴ n(S) = 4
(1) Event A: Getting at least one head
A = {HH, HT, TH}
∴ n(A) = 3
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{3}{4} \end{gathered}$$
Hence, the probability of getting at least one head is $\frac{3}{4}$.
(2) Event B: Getting no head
B = {TT}
∴ n(B) = 1
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{1}{4} \end{gathered}$$
​Hence, the probability of getting no head is $\frac{1}{4}$.