Question

consider an experiment of tossing a coin twice in a row. the probability of occurrence of two heads in a row is

Explanation:

Step1: Determine probability of one - head toss

The probability of getting a head in a single fair - coin toss is $\frac{1}{2}$, since there are 2 possible outcomes (head or tail) and 1 favorable outcome (head).

Step2: Use multiplication rule for independent events

The two coin - tosses are independent events. For independent events $A$ and $B$, the probability of both $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Here, let event $A$ be getting a head on the first toss and event $B$ be getting a head on the second toss. So $P(A) = P(B)=\frac{1}{2}$. Then $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$