Question

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome	$3{\text{ }}heads$	${\text{2 }}heads$	${\text{1 }}head$	${\text{No }}head$
Frequency	$23$	$72$	$77$	$28$

Find the probability of getting (i) $3{\text{ }}heads$, (ii) ${\text{2 }}heads$, (iii) ${\text{1 }}head$, (iv) ${\text{No }}head$.

Answer 1

This is the question of probability. We will use the basic formulas of probability here i.e. ratio of favourable event to the all possible event.

Formula Used: Probability of an event $P(E) = \dfrac{{Number{\text{ }}of{\text{ }}possible{\text{ }}or{\text{ }}favourable{\text{ }}event}}{{Total{\text{ }}possible{\text{ }}event}}$

Complete step by step solution: In this question, it is said that three coins are tossed simultaneously (means all together)$200$times,
So our total possible outcomes are = $200$
In the first part we have to calculate probability of getting $3$ heads,
From the given table we can see that the frequency of getting $3$ head is $23$.
Hence our favourable cases are $23$.
Therefore, Probability of getting three head is:
$P(E) = \dfrac{{23}}{{200}}$
This is our required answer.
In the second part we have to calculate probability of getting $2$ heads,
From the given table we can see that the frequency of getting $2$ head is $72$.
Hence our favourable cases are$72$.
Therefore, Probability of getting two head is:
$P(E) = \dfrac{{72}}{{200}} = \dfrac{9}{{25}}$ [ we divide both $72$ and $200$ by $8$]
This is our required answer.
In the third part we have to calculate probability of getting ${\text{1}}$ head,
From the given table we can see that the frequency of getting ${\text{1}}$ head is $77$.
Hence our favourable cases are $77$.
Therefore, Probability of getting one head is:
$P(E) = \dfrac{{77}}{{200}}$ [ we can’t simplify because they don’t have any common factor]
This is our required answer.
In the fourth part we have to calculate probability of getting no head,
From the given table we can see that the frequency of getting no head is $28$.
Hence our favourable cases are $28$.
Therefore, Probability of getting no head is:
$P(E) = \dfrac{{28}}{{200}} = \dfrac{7}{{50}}$ [we divide both terms by $4$ here]
This is our required answer.

Note: Don’t get confused with the name of the coins here, since three coins are tossed simultaneously, $200$ times so total cases are $200$. Also remember that the value of probability lies between $0$ and $1$, so your answer does not exceed $1$. Always check your answer.