# Experimental Probability

Flip a coin $10$ times and note down the result. Though you have an equal chance of getting either side, do you always get $5$ heads and $5$ tails out of $10$ trials?

Or, roll a die $60$ times and make a note of how many times you get a six. Will you always roll a six $10$ times?

In both cases, the answer is No!

Though the
*
theoretical
*
probability
of getting heads in the first example is
$\frac{1}{2}$
, and the
*
theoretical
*
probability of rolling a six in the second example is
$\frac{1}{6}$
, you may not get heads exactly
$\frac{1}{2}$
the time, and you may not roll a six exactly
$\frac{1}{6}$
of the time.

Suppose that, out of
$60$
rolls of the die, you roll a six
$7$
times. The fraction
$\frac{7}{60}$
is called the
**
experimental probability
**
. That is, the experimental probability of an event is the ratio of the number of favorable outcomes to the total number of trials.

With a fair coin or a fair die, you know the theoretical probability ahead of time. Experimental probability is useful in situations where you don't or can't know the probability of an outcome.

**
Example 1:
**

Suppose a volleyball team has won $3$ of its first $5$ matches. Then the experimental probability of its winning the next match is $\frac{3}{5}=0.6$ .

Suppose there are $11$ more matches left in the season. You can use the experimental probability to predict how many of these matches it will win.

$0.6\times 11=6.6$

So, you can expect that the volleyball team will probably win $6$ or $7$ of its next $11$ matches.

**
Example 2:
**

The table shows the results, after $20$ trials, of drawing one marble from a bag. Each marble drawn is replaced after noting down the color.

Red | Blue | Green | Yellow | Black |

$2$ | $5$ | $6$ | $4$ | $3$ |

What is the expected number of times that a blue marble will be drawn in $500$ draws?

We don't know the theoretical probability, because we aren't told how many marbles of various colors there are in the bag. But we do know that the experimental probability of drawing a blue marble is $\frac{5}{20}$ or $\frac{5}{20}$ . So, the expected number of times that a blue marble will be drawn in $500$ trials would be $\frac{1}{4}\times 500=125$ .