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Experimental Probability

Definition

Experimental probability is defined as the probability calculated on the basis of the results of an experiment.

For example, we know that on tossing a coin, the probability of getting heads is `1/2`. This is calculated theoretically and is thus called theoretical probability. Suppose you toss a coin a thousand times, and you get heads 470 times and tails 530 times. Then based on the results of this experiment, the probability of getting heads is `470/1000`. Since `470/1000` is the probability calculated from the results of an experiment, we call it "experimental probability". 

Further, we note that `1/2` is not equal to `470/1000`. Thus experimental probability is not always equal to the theoretical probability.

Formula

`P(A) = "Number of times you get the favorable result"/"Number of times the experiment is performed"`

Solved Examples

Problem 1

Out of ten running contests, Ginny got the first position in 8. What is the probability that she will get the first position in the next running contest?

Total number of running contests = 10
Number of contests in which Ginny got the first position = 8
Thus, applying the formula for experimental probability,
`P("first position in next contest") = "Number of contests in which Ginny got the first position"/"Total number of running contests"`
`P(first position in next contest") = 8/10 = 4/5`

Problem 2

On rolling a dice, a student got an even number six out of the ten times that he rolled the dice. What is the probability that he will get an even number on throwing the dice now?
  
Total number of times the dice is rolled = 10
Number of times that an even number occurred = 6
Thus, applying the formula for experimental probability,
`P(even number) = "Number of times that an even number occurred"/"Total number of times the dice is rolled"`
`P(even number) = 6/10 = 3/5`

Problem 3

In the last 30 days it rained on 20 days. What is the probability that it will rain today?

Number of days on which it rained = 20
Total number of days observed = 30
Thus, applying the formula for experimental probability,
`P("it will rain on next day") = "Number of days on which it rained"/"Total number of days observed"`
`P(it will rain on the next day") = 20/30 = 2/3`

Problem 4

Dan missed the school bus three out of five days a week. What is the probability that he will miss the school bus today?

Number of times Dan missed the school bus = 3
Total number of days = 5
Applying the formula for experimental probability,
`P("Dan will miss the bus today") = "Number of times he missed the school bus"/"Total number of days"`
`P("Dan will miss the bus today") = 3/5`

Problem 5 

Mrs. Sandy told Jimmy to get 12 eggs from the dairy farm. On the way home, Jimmy broke 5 on the twelve eggs. Then Mrs. Sandy told Jimmy to get one more egg. What is the probability that Jimmy will not break the egg this time?

Total number of eggs = 12
Number of eggs broken = 5
By the formula for experimental probability, the probability that Jimmy will break an egg is
`P("egg breaks") = 5/12`
The two events, that is, "the egg will break" and "the egg will not break" are complimentary events. Thus, the sum of their probabilities is 1.
The probability that Jimmy will not break an egg is
`P("egg does not break") = 1 - 5/12 = 7/12`

Exercise

Seventy eight out of a hundred students passed in an examination.

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