Question

Anushree has four coins A, B, C and D. One of these coins is a fair coin and the other three are biased coins. She throws each coin 200 times and records the number of times she gets a head. She gets the following data,
Coin A: 49 heads
Coin B: 142 heads
Coin C: 110 heads
Coin D: 68 heads
Pick the coin that is most likely to be the fair coin.

Answer 1

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.