Have you wondered what makes an event like rain random?
Step-by-step solution
Idea: An event is random when we cannot say for sure whether it will happen. Rain is random because it depends on too many changing factors to predict exactly, even though we know the possible outcomes (rain or no rain).
- Possible outcomes are known: on a given day it either rains or it does not rain.½ mark
- The result depends on many factors in the atmosphere: temperature, humidity, wind patterns and air pressure. A small change in any of them can change whether, when and where it rains.½ mark
- Because rain is so sensitive to these factors, it is impossible to know with absolute certainty whether it will rain on a particular day, at a particular time and place. That uncertainty is what makes rain random.½ mark
- What we can do is estimate the likelihood. Weather offices study patterns in data from many past days with similar conditions and give a probability, such as “a 70% chance of rain” (probability 0.7).½ mark
Check: A “70% chance of rain” forecast means: on many past days with conditions like today’s, it rained on about 70 out of 100 of them. It does not promise rain today.
Answer to write in the exam
Possible outcomes: rain / no rain.
Rain depends on many complex atmospheric factors: temperature, humidity, wind patterns, pressure.
It is very sensitive to these factors, so it cannot be predicted with total certainty.
∴ Rain is a random event; only its probability can be estimated from past data.
Common mistakes that cost marks
- Saying rain is random because “nobody knows the possible outcomes”. The outcomes are known (rain or no rain); it is the actual result that cannot be known for sure.
- Thinking a forecast of “80% chance of rain” is wrong if it stays dry. Probability 0.8 still leaves a 0.2 chance of no rain.
- Saying rain has nothing to do with mathematics. Probability is how scientists measure and compare the chance of rain.
How this can come in the exam
A weather report says there is a 30% chance of rain tomorrow. As a probability, this is
- 30
- 3
- 0.3
- 0.03
Show answer
(C) 0.3
30% = 30100 = 0.3.
The forecast for Saturday is “90% chance of rain”. It does not rain on Saturday. Was the forecast wrong? Explain.
Show answer
Not necessarily. A 90% chance means probability 0.9, so there is still a 0.1 (10%) chance of no rain. Rain is random, so the forecast gives the likelihood, not a certainty. A forecast can only be judged over many days: on about 90 out of 100 such days it should rain.Try one yourself
Give two factors in the atmosphere that make rainfall hard to predict exactly, and say what kind of statement a weather forecaster can give instead.
Show answer
Any two of: temperature, humidity, wind patterns, air pressure. The forecaster gives a probability, for example “60% chance of rain” (0.6), based on patterns in past data.
More questions like this
- 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.
- Suppose you roll a die 50 times, and it lands on a 4 exactly 8 times.
- If you roll a standard 6-sided die, what is the theoretical probability of getting a 4?