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.
- (i) The next Monday will come after Sunday.
- (ii) It will snow in Mumbai in July.
- (iii) An elephant will walk through your classroom today.
- (iv) You will greet at least one friend at school tomorrow.
Step-by-step solution
Idea: Ask two things for each event: can it happen at all, and if so, is it nearer to never or nearer to always? Probability 0 means it cannot happen, 1 means it must happen, and 0.5 means it is as likely to happen as not.
(i) The next Monday will come after Sunday.
- The days of the week always follow the same order, and Monday always comes straight after Sunday. There is no other possibility.½ mark
(ii) It will snow in Mumbai in July.
- Mumbai is a warm coastal city at sea level, and July is the hot, rainy monsoon month there. Snow needs freezing temperatures, which Mumbai never reaches; it has never snowed there.½ mark
(iii) An elephant will walk through your classroom today.
- It is not strictly impossible (elephants exist, and in some places they are walked through towns), but it almost never happens in a school. So the chance is very small, close to 0.½ mark
(iv) You will greet at least one friend at school tomorrow.
- On a normal school day you meet many friends, so this nearly always happens. It is not certain, because you could be ill, or tomorrow could be a holiday. So the chance is high, close to 1.½ mark
Check: Read the scale back: an event at 0 must never happen (true for snow in Mumbai in July) and an event at 1 must always happen (true for Monday after Sunday). The two in between can happen but are not guaranteed, so they are strictly between 0 and 1.
Answer to write in the exam
(i)
Monday always comes immediately after Sunday.
∴ Certain (1)
(ii)
Mumbai is warm all year; July is the monsoon; it never snows there.
∴ Impossible (0)
(iii)
Possible but almost never happens.
∴ Less likely (close to 0)
(iv)
Happens on almost every school day, but not certain (absence, holiday).
∴ More likely (close to 1)
Common mistakes that cost marks
- Calling the elephant event “impossible”. It is extremely unlikely but could happen, so it is less likely, just above 0. Keep 0 for things that cannot happen at all.
- Calling event (iv) “certain”. You might be absent or it might be a holiday, so it is more likely, not certain.
- Giving labels with no reasons. The question asks for a reason for each ranking; a label alone loses marks.
How this can come in the exam
Which of the following events has probability 0?
- Getting a 7 on one throw of an ordinary die
- Getting a 6 on one throw of an ordinary die
- Getting heads when a coin is tossed
- The next day after Friday being Saturday
Show answer
(A) Getting a 7 on one throw of an ordinary die
An ordinary die has faces 1 to 6, so a 7 can never come up: impossible, probability 0. The last option is certain (probability 1).
Assertion (A): The probability that a month chosen from the calendar has 32 days is 0.
Reason (R): The probability of an impossible event is 0.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(A) Both A and R are true, and R is the correct explanation of A.
No month has 32 days, so the event is impossible and its probability is 0. R is true and is exactly the reason for A.
Try one yourself
Label each event as impossible, less likely, even chance, more likely or certain: (a) February next year will have 30 days. (b) A tossed coin lands tails. (c) It will be dark at midnight tonight in your town.
Show answer
(a) Impossible (February has 28 or 29 days). (b) Even chance (heads and tails are equally likely). (c) Certain (midnight is always at night, so it is dark).
More questions like this
- 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?
- A letter is picked at random from the word ‘PROBABILITY’. What is the probability of picking the letter B?
- Suppose you anonymously collect information regarding the favourite fruit of 50 students in your class. Let us assume that the results are: 20 students like mango, 15 students like apples, 10 students like bananas, and 5 students like grapes. Let us play a game! Suppose we randomly pick one student from the class and try to guess their favourite fruit. What’s the probability that the student’s favourite fruit is mango?