Page 305 - Start Up Mathematics_7

Experimental Probability
When a probability is determined by observing the outcomes of an experiment, it is said to be
determined experimentally or empirically. Let’s find the number of heads obtained when a coin
is tossed 10 times and tabulate the result as follows:
Extension
Head 7 Theoretical or classical probability

Tail 3 is applicable under ideal conditions
when outcomes are equally likely.

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Out of 10 trials, head appears 7 times. This gives the probability of head as , which is nowhere
10
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near the theoretical probability of head which is . This anomaly is due to the fact that experimental
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probability comes closer and closer to theoretical probability only in the long run, i.e., more the
number of trials, the better is the estimate of experimental probability.
Conduct an activity of tossing a coin 100 times and observe the number of heads. You will observe
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the probability of head is nearer to . Ask your friends to toss a coin 100 times each. What are
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their probabilities? Collect the data of all your friends and find the probability of head if the coin is
tossed 200 times, 300 times, 400 times, ..., and so on. You will agree to the fact that as the number
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of trials increases, the experimental probability of head comes closer and closer to .
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The Experimental Fact
• During World War II, John Kerrich, a prisoner of war, tossed a coin 10,000 times out of
which he obtained head 5,067 times.

• An English statistician Karl Pearson tossed a coin 24,000 times and got 12,012 heads.
• As the number of tosses increases, the number of heads and tails comes closer to half.

EXERCISE

1. Describe the chances of occurrence of the following events using the words: impossible,
not likely, equally likely, most likely, certain

(a) A red marble picked up at random from a bag containing 8 red marbles and 2 black marbles
(b) The chances of getting tail in a toss of a coin

(c) The chances of India winning a toss
(d) You will grow over 100 feet tall

(e) A year having 12 months
(f) All 10 traffic signal lights enroute to school will be green
2. Find the probabilities of the following events:

(a) A rupee (`) worth 100 paise (b) February always having 29 days
(c) May having 31 days (d) A cat giving birth to a lion

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