Can we predict these outcomes with 100% certainty?
Step-by-step solution
To find: Whether the outcome of each situation can be predicted with complete certainty
Idea: A situation is random when we know every outcome that could happen but not the one that will happen. For random situations we cannot be 100% sure; we can only measure how likely each outcome is. That measure is called probability.
- List the possible outcomes.
Rain: it rains or it does not rain.
Hockey match: our team wins, draws or loses.
Lucky draw: any one of the students is chosen.½ mark - Ask: do we know which one will happen? No. The weather depends on many changing conditions, the match depends on how both teams play on the day, and the slip is picked without looking. There is an element of chance in each.½ mark
- So we cannot predict these outcomes with 100% certainty. What we can do is describe how likely each outcome is, using words such as impossible, less likely, equally likely, more likely and certain, based on the evidence we have (for example, a bright sunny sky makes rain less likely).1 mark
Check: A quick test for randomness: could you write down the result before it happens and be sure you are right? For rain, the match and the lucky draw, the answer is no, so they are random.
Answer to write in the exam
Possible outcomes: rain / no rain; win / draw / lose; any one student chosen.
Which outcome will occur is not known in advance (element of chance).
∴ No, these outcomes cannot be predicted with 100% certainty; only their likelihood can be judged (impossible, less likely, equally likely, more likely, certain).
Common mistakes that cost marks
- Saying “Yes, we can predict rain because the sky is cloudy.” Clouds make rain more likely, not certain. Evidence changes the likelihood; it does not remove the chance.
- Thinking that “random” means “anything can happen”. In a random situation the possible outcomes are known (win, draw, lose); only the actual result is unknown.
- Answering just “No” with no reason. Examiners expect the reason: the outcomes are known but which one will happen is not.
How this can come in the exam
Which of the following is a random event?
- The sun rising in the east tomorrow
- Water boiling at 100 °C at sea level
- Getting a 5 when a die is thrown
- Sunday coming after Saturday
Show answer
(C) Getting a 5 when a die is thrown
A die can show 1, 2, 3, 4, 5 or 6, and we cannot know in advance which face will come up. The other three are certain.
A class teacher writes the names of all 40 students on slips, folds them and picks one slip without looking. Explain why the name picked cannot be predicted, and name the possible outcomes.
Show answer
The possible outcomes are the 40 names (every student could be picked). The slips are folded and picked without looking, so nothing tells us which name will come out; each student has the same chance. Because the outcomes are known but the result is not, the draw is random and cannot be predicted with certainty.Try one yourself
Can you predict with 100% certainty which team will win the toss before a football match? Give a reason.
Show answer
No. The toss has two known outcomes (heads or tails), but which side will land up cannot be known before the coin falls. Each captain has an equal chance.
More questions like this
- Such unpredictability can be useful sometimes! For example, in a cricket match, the fact that a coin is tossed to decide which team will bat first is considered to be a fair method. Can you explain why?
- Have you wondered what makes an event like rain random?
- Ask your friend to predict the outcome of a ₹ 1 coin you toss. Do you see that your friend could guess heads or tails but could not know for certain? That’s randomness! All possible results are known, but each individual try is unpredictable.
- Rank the following events on a scale from 0 (Impossible) to 1 (Certain). Label each event: Impossible, less likely, equally likely (even chance), more likely, certain. Give reasons why you gave each event its ranking.
- The set of all possible outcomes in an experiment is called the sample space. The sample space may be listed within brackets, separated by commas as shown below.