Question

What is the probability of $2$ heads in a row?

Answer 1

The probability of an event is,

$P\left(E\right)=\frac{Numberoftimesaneventoccurs}{Totalnumberoftrials}$

When a coin is tossed, the possible outcomes are a head and a tail.

So, the probability of getting a head is,

$P\left(head\right)=\frac{1}{2}$

We get,

Probability of getting $2$ heads in a row $=$ Probability of getting the head first-time $\times$ Probability of getting the head second-time

$\Rightarrow$ Probability of getting $2$ heads in a row $=P\left(head\right)\times P\left(head\right)$

$\Rightarrow$ Probability of getting $2$ heads in a row $=\frac{1}{2}\times \frac{1}{2}$

$\Rightarrow$ Probability of getting $2$ heads in a row $=\frac{1}{4}$

Hence, the probability of $2$ heads in a row is $\frac{1}{4}$.