Exercise 7.1 Practice
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Overview
This page provides comprehensive Ch 7: The Mathematics of Maybe: Introduction to Probability - Exercise Set 7.1 Practice. Practice ranking real-world events on the 0 to 1 scale from impossible to certain with step-by-step explanations.
Probability Scale & Likelihood Ranking
Q1: Event Likelihood Ranking
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**, or **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.
(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.
(i) The next Monday will come after Sunday:
• **Label:** Certain
• **Probability Value:** $1$
• **Reason:** Days of the week follow a fixed, immutable cyclical sequence. Monday always succeeds Sunday without exception.
• **Label:** Certain
• **Probability Value:** $1$
• **Reason:** Days of the week follow a fixed, immutable cyclical sequence. Monday always succeeds Sunday without exception.
(ii) It will snow in Mumbai in July:
• **Label:** Impossible
• **Probability Value:** $0$
• **Reason:** July is a monsoon summer month in Mumbai (a tropical coastal city) where temperatures never drop anywhere near freezing point.
• **Label:** Impossible
• **Probability Value:** $0$
• **Reason:** July is a monsoon summer month in Mumbai (a tropical coastal city) where temperatures never drop anywhere near freezing point.
(iii) An elephant will walk through your classroom today:
• **Label:** Less likely
• **Probability Value:** Close to $0$ (but not strictly 0, as a wild escape or special event is technically possible, though highly improbable).
• **Reason:** School buildings are situated in urban/suburban zones far from wildlife habitats, and classroom doorways are not suited for large animals.
• **Label:** Less likely
• **Probability Value:** Close to $0$ (but not strictly 0, as a wild escape or special event is technically possible, though highly improbable).
• **Reason:** School buildings are situated in urban/suburban zones far from wildlife habitats, and classroom doorways are not suited for large animals.
(iv) You will greet at least one friend at school tomorrow:
• **Label:** More likely
• **Probability Value:** High (close to $1$).
• **Reason:** Schools are social environments where students interact, meet friends daily, and actively exchange greetings.
• **Label:** More likely
• **Probability Value:** High (close to $1$).
• **Reason:** Schools are social environments where students interact, meet friends daily, and actively exchange greetings.
(i) Certain (1)
(ii) Impossible (0)
(iii) Less likely (close to 0)
(iv) More likely (high probability)