Question

A coin is tossed successively two times. Find the probability of getting both heads, getting both tails, both heads or both tails

Answer 1

Step 1: Find the sample space for tossing a coin twice:

Sample space for throwing a coin successively two times,

$$\begin{gathered} n\left(S\right)={\text{(number of possible outcomes of tossing a coin)}}^{\text{number of times coins tossed}} \\ n\left(S\right)={\left(2\right)}^2 \\ n\left(S\right)=4 \end{gathered}$$

Thus, the sample space of tossing a coin two times successively will be,

$S_1=\{HH,HT,TH,TT\}$

Step 2: Find the probability of getting both heads:

The favourable outcome of getting both heads will be $\left\{HH\right\}$.

The formula for probability will be,

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$\text{Probability=}\frac{1}{4}$

Step 3: Find the probability of getting both tails:

The favourable outcome of getting both heads will be $\left\{TT\right\}$.

The formula for probability will be,

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$\text{Probability=}\frac{1}{4}$

Step 4: Find the probability of getting both heads or both tails:

The favourable outcome of getting both heads will be $\left\{HH\right\}$.

The favourable outcome of getting both heads will be $\left\{TT\right\}$.

The formula for probability will be,

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$$\begin{gathered} \text{Probability=}\frac{2}{4} \\ \text{=}\frac{1}{2} \end{gathered}$$

Final answer:

Hence, the probability of getting both heads $=\frac{1}{4}$, getting both tails $=\frac{1}{4}$, both heads or both tails$=\frac{1}{2}$.