Two coins are tossed simultaneously. Find the probability of getting Head on one coin and Tail on the other coin.

Hint: First, find the sample space of the problem. Next, find the number of elements in the sample space = total number of outcomes. Now, let E be an event when the head appears on one coin and the tail on another coin. Find the set E and find the number of elements in the sample space = total number of outcomes. Next, use the formula: $P(E)=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$ to get the final answer.

Complete step-by-step answer:

In this question, we are given that two fair coins are tossed simultaneously.

We need to find the probability of getting Head on one coin and Tail on the other coin.

When two coins are tossed simultaneously, the sample space is given by : S = {HH, HT, TH, TT} where, H is the appearance of Head and T is the appearance of the Tail on the coin.
So, the number of elements in the sample space = total number of outcomes is given by the following:

n (S) = 4

Let E be an event when the head appears on one coin and the tail on another coin. E:{HT,TH}
So, the number of elements in the E = number of favourable outcomes is given by the following:

n (E) = 2

Now, we know that probability of an event is equal to the number of favourable outcomes divided by the total number of outcomes. i.e. $P(E)=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$

Using the above formula, we will get the following:

$P(E)=\dfrac{2}{4}=\dfrac{1}{2}$

Hence, the probability of getting Head on one coin and Tail on the other coin is equal to $\dfrac{1}{2}$.

This is the final answer.

Note: In this question, it is very important to know what a sample space is. In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.