Answer
Verified
376.5k+ views
Hint: Using the concept of probability, we must first find the theoretical data, as to how many heads will appear when a fair coin is tossed 200 times. We then have to compare all the values given in the question to our theoretical data, and check which one is closest, or most precise. This coin is most likely to be the fair coin.
Complete step-by-step solution:
We know that in a fair coin, there are two possible outcomes, head and tail. And so, we can say that the probability of occurrence of head for a single throw of a fair coin is,
$P\left( H \right)=\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}}$
$P\left( H \right)=\dfrac{1}{2}$.
So, we can say that, in an ideal situation,
Number of heads when a fair coin is tossed 200 times = $200\times \dfrac{1}{2}=100$.
So, theory suggests that we should get 100 heads when a fair coin is tossed 200 times.
But we also know that experimental data may vary with a small margin. And the number of heads we get in reality may be different from the value 100.
Thus, we can say that the value which is most precise to the value 100 is most likely to be the fair coin.
Here, the number of heads is given to be 49, 142, 110 and 68. We can clearly see that the value 110 is most precise to 100.
Hence, coin C is most likely to be the fair coin.
Note: We must understand that, in this question, it is not possible to predict the fair coin with 100% accuracy. That is why, we are saying that coin C is ‘most likely’ to be a fair coin. We must also understand that precision indicates how close the data points are to one another.
Complete step-by-step solution:
We know that in a fair coin, there are two possible outcomes, head and tail. And so, we can say that the probability of occurrence of head for a single throw of a fair coin is,
$P\left( H \right)=\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}}$
$P\left( H \right)=\dfrac{1}{2}$.
So, we can say that, in an ideal situation,
Number of heads when a fair coin is tossed 200 times = $200\times \dfrac{1}{2}=100$.
So, theory suggests that we should get 100 heads when a fair coin is tossed 200 times.
But we also know that experimental data may vary with a small margin. And the number of heads we get in reality may be different from the value 100.
Thus, we can say that the value which is most precise to the value 100 is most likely to be the fair coin.
Here, the number of heads is given to be 49, 142, 110 and 68. We can clearly see that the value 110 is most precise to 100.
Hence, coin C is most likely to be the fair coin.
Note: We must understand that, in this question, it is not possible to predict the fair coin with 100% accuracy. That is why, we are saying that coin C is ‘most likely’ to be a fair coin. We must also understand that precision indicates how close the data points are to one another.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE