Question

The probability of getting head and tail alternatively in $3$ throws of a coin is,

• A. $\frac{1}{8}$
• B. $\frac{1}{4}$
• C. $\frac{1}{3}$
• D. $\frac{3}{8}$

Answer 1

The correct option is B

$\frac{1}{4}$

Calculate the probability

Whenever, a coin throws, there are always two possibilities of getting either heads or tails.

Now, we throws a coin $3$ times,

So the possible outcomes which satisfies the conditions are

$$\begin{gathered} =2^3 \\ =8 \end{gathered}$$

Here ,the space of all outcomes$=\{\left(HHH\right),\left(HHT\right),\left(HTH\right),\left(HTT\right),\left(THH\right),\left(THT\right),\left(TTH\right),\left(TTT\right)\}$

Where, $H$ denotes head and $T$ denotes tail

Now, the favourable outcome of getting heads and tails alternatively$=\{\left(HTH\right),\left(THT\right)\}$

$\mathrm{Probability}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{outcomes}}$

$\mathrm{Probability}=\frac{2}{8}=\frac{1}{4}$

Therefore, probability of getting head and tail alternatively in $3$ throws of a coin is $\frac{1}{4}$, so option (B) is the correct answer.