Question

In a throw of two coins, find the probability of getting both heads or both tails.

Answer 1

Step 1: Find the number of possible and favourable outcomes

We know that when two coins are tossed together a possible number of outcomes are

$\mathit{}\mathit{\{}\mathit{}HH\mathit{,}TH\mathit{,}HT\mathit{,}TT\mathit{}\mathit{\}}$

Thus, total number of outcomes i.e.,$n\left(S\right)=4$

Let , E be the event of getting both heads or both tails

$E=\{HH,TT\}$

Thus, total number of favourable outcomes i.e.,$n\left(E\right)=2$

Step 2: Use the formula for probability

We know that, probability of an event $E$is given by,

$Probability=\frac{n\left(E\right)}{n\left(S\right)}$

$$\begin{gathered} \Rightarrow P\left(E\right)=\frac{2}{4} \\ =\frac{1}{2} \end{gathered}$$

Final answer:

Therefore, Ina throw of two coins, the probability of getting both heads or both tails is $\frac{1}{2}$.