Question

Find the probability distribution of the number of heads in two tosses of a coin.

Answer 1

Now we know that the outcome of a coin toss can be heads or tails. Hence first we will list all the possible outcomes of the event when two coins are tossed. Now we will calculate the probability such that we get 0 Heads, 1 Heads and 2 heads. Now since we know the probability of each case we will create the corresponding probability distribution Table.

Complete step by step answer:
Now let us say a coin is tossed twice.
Now for each coin the outcomes can be heads or tails.
Hence when two coins are tossed the number of possible outcomes are.
First coin shows heads, the second one also shows heads (HH).
First coin shows Heads but the second one shows Tails.
First coin shows Tails but the second coin shows Heads
First coin shows Tails as we as the second coin also shows Tails.
Let us say that set S is the set of all possibilities
S = {HH, HT, TH, TT}
Hence we have total outcome is 4.
Hence we have either there are 0 Heads or there is 1 Heads or there are 2 Heads in the outcome.
Let us calculate the probability of getting 0 Heads.
Now the only outcome in which we can get 0 Heads is TT.
We know that probability $=\dfrac{\text{number of required outcome}}{\text{number of total outcome}}$
Hence the probability of getting 0 heads is $\dfrac{1}{4}$ .
Now we will calculate the probability of getting 1 Heads.
Now the only outcomes in which we can get 1 Heads are HT and TH
We know that probability $=\dfrac{\text{number of required outcome}}{\text{number of total outcome}}$
Hence the probability of getting 1 heads is $\dfrac{2}{4}=\dfrac{1}{2}$
Now let us calculate the probability of getting 2 Heads.
Now the only outcome in which we can get 2 Heads is HH.
We know that probability $=\dfrac{\text{number of required outcome}}{\text{number of total outcome}}$
Hence the probability of getting 2 heads is $\dfrac{1}{4}$ .
Hence we get

Number of Heads	0	1	2
Probability	$\dfrac{1}{4}$	$\dfrac{1}{2}$	$\dfrac{1}{4}$

Note: Now note that while calculating probability we need not make use of the fact that probability of getting heads or tails is $\dfrac{1}{2}$ . Also note that probability distribution is nothing but the corresponding probabilities of all the possible events of given condition. Do not confuse it with any other distribution tables in statistics.