LEARN · EXPLAIN · REVISE

Find the missing probability p.

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 / Foundation#Your turn

X\in\{0,5,6\};\quad P=(1/4,p,1/2)

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.

1/4+p+1/2=1

Worked solution

The requested value is 0.25.

Checks and common pitfalls: Normalisation determines the remaining probability.

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.