Question

A coin is tossed 10,000 times and head turns up 5,195 times. Is the coin unbiased?

Answer 1

YES THE COIN UNBIASED .

Answer 2

The coin is not unbiased.

Given,

A coin is tossed 10,000 times and head turns up 5,195 times.

To Find,

Is the coin unbiased?

Solution,

We can solve the question as follows:

It is given that a coin is tossed  10,000 times and head turns up 5,195 times. We have to find out if it is unbiased or not.

The probability of getting a head in one toss is:

$p = \frac{1}{2}$

The expected number of heads in 10000 tosses will be:

$np = 10000*\frac{1}{2} = 5000$

In the question, it is given that head turns up 5195 times.

The deviation of the actual number of heads from the expected number of heads will be:

$Deviation = Actual\: - Expected$

                 $= 5195 - 5000$

                 $= 195$

Now, the formula for finding the standard deviation is:

$Standard\: deviation = \sqrt{npq}$

Where, $p = Probability\: of\: the\: event\: not\: occurring$

Substituting the values,

$Standard\: deviation = \sqrt{10000*\frac{1}{2} *\frac{1}{2} }$

                               $= \sqrt{2500} = 50$

Now,

$\frac{195}{50} = 3.9$

The deviation of 195 is 3.9 times the standard deviation, which is greater than 3.

Hence, the coin can be biased.

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