Login/Sign Up
Home » A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and be the event on the die’. Check whether and are independent events or not.
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and \mathrm{B} be the event { }^{\prime} 3 on the die’. Check whether \mathrm{A} and \mathrm{B} are independent events or not.
CBSE | Maths | NCERT | Probability
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and \mathrm{B} be the event { }^{\prime} 3 on the die’. Check whether \mathrm{A} and \mathrm{B} are independent events or not.

Given: A fair coin and an unbiased die are tossed.

Let A be the event head appears on the coin. So the sample space of the event will be:

\Rightarrow A={(\mathrm{H}, 1),(\mathrm{H}, 2),(\mathrm{H}, 3),(\mathrm{H}, 4),(\mathrm{H}, 5),(\mathrm{H}, 6)}

\Rightarrow P(A)=6 / 12=1 / 2

Now, Let B be the event 3 on the die. So the sample space of event will be:

\Rightarrow \mathrm{B}={(\mathrm{H}, 3),(\mathrm{T}, 3)}

The probability of the event will be \Rightarrow P(B)=2 / 12=1 / 6

As, A \cap \mathrm{B}={(\mathrm{H}, 3)}

Thus evaluating the value of parameter required to proof that the events are independent.

\Rightarrow \mathrm{P}(\mathrm{A} \cap \mathrm{B})=1 / 12 \ldots \ldots (1)

And
P(A) . P(B)=1 / 2 \times 1 / 6=1 / 12 \ldots \ldots . .(2)

From (1) and (2) P(A \cap B)=P (A). P(B)

Therefore, A and B are independent events.

i

More Material