Probability
ICSE Class 8 · Mathematics · Chapter 23
What this chapter covers
- Chance in everyday life
- Random experiments, outcomes and events
- The probability scale from 0 to 1
- Experiments with coins
- Experiments with dice
- Equally likely outcomes and the expected chance
- Chance in a passage of writing
- Making predictions from past results
- Chance in life events
Key points
- Probability is a number from 0 to 1 that measures how likely an event is; a larger number means a more likely event.
- An impossible event has probability 0, a certain event has probability 1, and an event near (1)/(2) is as likely to happen as not.
- A random experiment has known possible outcomes but an unpredictable result; each single performance is a trial.
- Experimental probability = number of trials in which the event happened ÷ total number of trials.
- The probabilities of an event happening and not happening add up to 1.
- With many trials, the experimental probability settles near a fixed value: about (1)/(2) for each face of a fair coin and (1)/(6) for each face of a fair die.
- Throwing many identical coins or dice together and adding the results is a quick way to collect a large number of trials.
- When outcomes are equally likely, expected probability = number of favourable outcomes ÷ total number of outcomes.
- Expected number of times an event happens = probability × number of trials.
- Each trial is independent: a coin or die has no memory, and unlikely events still happen sometimes.
Questions answered
What is a random experiment? Give one example from home.
A random experiment is an action whose possible results are known but whose actual result cannot be predicted in advance. Example: picking one shirt from a pile without looking.
List the outcomes when a fair die is thrown once. How many outcomes are in the event "a number greater than 2"?
The outcomes are 1, 2, 3, 4, 5 and 6. The event "greater than 2" has 4 outcomes: 3, 4, 5 and 6.
Which of these cannot be a probability: 0.4, 1.2, (7)/(8), 0, -0.1, 100%?
1.2 and -0.1, because every probability lies from 0 to 1. (100% equals 1, so it is allowed.)
A coin is tossed 60 times and shows tails 33 times. Find the experimental probability of heads.
Heads appeared 60 - 33 = 27 times, so the probability is (27)/(60) = 0.45.
Neha says, "My coin has landed heads six times in a row, so the next toss will surely be tails." Is she right? Explain briefly.
No. A coin has no memory, so the probability of tails on the next toss is still (1)/(2).
A fair die is thrown once. Find the probability of getting (a) a 2, (b) an odd number, (c) a number less than 1.
(a) (1)/(6); (b) (3)/(6) = (1)/(2); (c) 0, because it is impossible.
A box holds 4 mango toffees and 6 orange toffees. One is picked without looking. Find the probability that it is a mango toffee.
(4)/(10) = (2)/(5), or 0.4.
Why does a class get a more dependable value for the probability of heads by tossing 10 coins each than by one student tossing one coin 20 times?
The class collects far more trials, and with more trials the experimental probability settles down close to its true value.