LEARN · EXPLAIN · REVISE

A fair die is rolled; X=1 for a face at most d, and X=0 otherwise. Find P(X=0).

Read the idea, work independently, then explain what changed.

高三選擇性必修第三册(A版).pdf · 7.2 · PDF 61 / printed page 56

TOPIC 01

Discrete random variables and distributions

Construct a distribution and compute event probabilities from its support.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

d=3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List the possible values and probabilities before computing moments.

Hint 2

Count faces strictly above d.

Worked solution

The requested value is 0.5.

Checks and common pitfalls: Different die faces are grouped into one binary value.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Defining relation: Construct a distribution and compute event probabilities from its support.
$\sum_xP(X=x)=1$
Conditions: Every probability lies in [0,1]; values and events must not be double-counted.