Question: When \[2\] coins are tossed simultaneously, what are the possible outcomes? In a single throw of \[2...

Question

When $2$ coins are tossed simultaneously, what are the possible outcomes? In a single throw of $2$ coins, what is the possibility of getting at least one head?

Answer 1

Solution

We will first find the set of outcomes when a single coin is tossed. Then, we will find the combinations of outcomes when $2$ coins are tossed simultaneously. Next, we will select those outcomes which have at least one head. Finally, we will find the probability of getting at least one head using the probability formula.

Formula used:
If $A$ is an event, then $P(A) = \dfrac{{n(A)}}{{n(S)}}$ , where $n(A)$ is the number of outcomes favourable to the event $A$ and $n(S)$ is the number of all possible outcomes.

Complete step by step solution:
We know that when a coin is tossed, there are only two possible outcomes which are Head and a Tail.
Let us denote Head by $H$ and Tail by $T$ . Let the set of outcomes of a single coin toss be $\\{ H,T\\}$ . We are supposed to find the outcomes when $2$ coins are tossed simultaneously.
We can do this by taking combinations of outcomes.
Suppose the first coin shows a head and the second coin shows a head as well. Then the outcomes in this toss will be $HH$ .
Similarly, we can find the other outcomes.
Thus, the possible outcomes when two coins are tossed simultaneously are $\\{ HH, HT, TH, TT \\}$ .
Now, we have to find the probability of getting at least one head. This means that we have to select outcomes which have a minimum of one head.
Therefore, the favourable outcomes are $\\{ HH,HT,TH\\}$ .
Let $A$ be the event of getting at least one head. Then, $n(A) = 3$ and $n(S) = 4$ .
So, the probability is $P(A) = \dfrac{{n(A)}}{{n(S)}} = \dfrac{3}{4}$

Therefore, the probability of getting at least one head is $\dfrac{3}{4}$ .

Note:
There is a significant difference between the terms “outcome” and “favourable outcome”. An outcome is simply the result of an experiment. A favourable outcome is the outcome which we desire to get with respect to a particular experiment. In the given problem, the outcomes of tossing $2$ coins are $\\{ HH, HT, TH, TT\\}$ but the favourable outcomes $\\{ HH, HT, TH\\}$ are the outcomes we desire to get at least one head. In addition, it must be noted that the probability of any event is a value that lies between 0 and 1.