Answer
$\dfrac{1}{2048}$
Work Step by Step
As per the definition of in-dependency, we can write
$P(A_1 \cap A_2 \cap..........\cap A_{11})=P(A_1) P(A_2) .........P(A_{11})$
Here, $A_1,A-2, ........,A_{11}$ denotes the events that the toss of the first coin is head.
Since, $P(A_{i})=\dfrac{1}{2}$
So, $P(A_1 \cap A_2 \cap..........\cap A_{11})=(\dfrac{1}{2}) \times (\dfrac{1}{2}) \times.........\times (\dfrac{1}{2})$
or, $=\dfrac{1}{2^{11}}$
or, $=\dfrac{1}{2048}$
