Flip a coin times and note down the result. Though you have an equal chance of getting either side, do you always get heads and tails out of trials?
Or, roll a die times and make a note of how many times you get a six. Will you always roll a six times?
In both cases, the answer is No!
Though the theoretical probability of getting heads in the first example is , and the theoretical probability of rolling a six in the second example is , you may not get heads exactly the time, and you may not roll a six exactly of the time.
Suppose that, out of rolls of the die, you roll a six times. The fraction 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.
Suppose a volleyball team has won of its first matches. Then the experimental probability of its winning the next match is .
Suppose there are more matches left in the season. You can use the experimental probability to predict how many of these matches it will win.
So, you can expect that the volleyball team will probably win or of its next matches.
The table shows the results, after trials, of drawing one marble from a bag. Each marble drawn is replaced after noting down the color.
What is the expected number of times that a blue marble will be drawn in 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 or . So, the expected number of times that a blue marble will be drawn in trials would be .