4-Sided Die: Conditional Probability

Problem 2.2 • Calculate P(X₁ = x | Min = m) or P(X₁ = x | Max = M)

🎲 Scenario: Roll a 4-sided die twice, getting outcomes X₁ and X₂.

❓ Question: Given information about the minimum or maximum of the two rolls, what is the conditional probability of a specific first roll value?

🎯 Sample Space (16 outcomes)

X₂=1

X₂=2

X₂=3

X₂=4

Condition Met (B)

Event A ∩ B

Conditional Probability

P(X₁ = 2 | Min = 2) = |A ∩ B| / |B|

3/5

= 0.6000

⚙️ Select Condition

Condition Type

Condition Value

Query: X₁ = ?

📊 Current Selection

Outcomes in B

Outcomes in A ∩ B

💡 Formula

P(A|B) = P(A ∩ B) / P(B)
= |A ∩ B| / |B|