LEARN · EXPLAIN · REVISE

Find p when P(X=0)=p, P(X=1)=2p and P(X=2)=tp.

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 / Standard#Worked example

t=3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List the possible values and probabilities before computing moments.

Hint 2

Use this intermediate relation.

p+2p+tp=1

Worked solution

The requested value is 0.166666666667.

Checks and common pitfalls: Check all resulting probabilities are nonnegative.

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.