The Mathematics of Maybe: Introduction to Probability | Exercise 7.1

Question 1

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.

Solution

Understand the Question

Probability measures how likely an event is to happen, represented on a scale from $0$ $0$ to $1$ $1$ :
- $0$ (Impossible): The event can never occur.
- Less likely: Probability between $0$ and $0.5$ .
- Equally likely (Even chance): Probability is exactly $0.5$ .
- More likely: Probability between $0.5$ and $1$ .
- $1$ (Certain): The event is guaranteed to happen.

(i) The next Monday will come after Sunday.

Step 1 · Determine the Likelihood

In our calendar system, the days of the week follow a fixed, unchanging sequence. Monday always immediately follows Sunday, so this event is guaranteed to happen.

Answer

(i) Certain (Probability $= 1$ )

(ii) It will snow in Mumbai in July.

Step 1 · Determine the Likelihood

Mumbai has a tropical climate where July brings hot, humid monsoon weather with temperatures far above freezing. Since snowfall requires below-freezing temperatures, this event cannot happen.

Answer

(ii) Impossible (Probability $= 0$ )

(iii) An elephant will walk through your classroom today.

Step 1 · Determine the Likelihood

Classrooms are enclosed indoor school spaces where large wild animals like elephants do not enter under any normal circumstances, making this event practically impossible.

Answer

(iii) Impossible (Probability $= 0$ )

(iv) You will greet at least one friend at school tomorrow.

Step 1 · Determine the Likelihood

Greeting friends is a standard daily social occurrence when going to school, making it highly probable. However, unexpected situations (like absence or illness) mean it is not $100\%$ guaranteed.

Answer

(iv) More likely (Probability is close to $1$ )

Common Mistakes

Confusing 'More likely' with 'Certain': An everyday, highly probable event (like greeting a friend) is more likely, not certain, because unexpected circumstances can still prevent it.
Equating highly rare with 'Less likely': Events that are physically or practically impossible in given conditions (like snow in tropical Mumbai in July) have a probability of exactly $0$ (Impossible).