Math Problem Statement

Solve

When two teams A and B play a game, the probability that A wins the game is 50% and the probability that B wins the game is 40%. If the two teams play this game three times, find the probability that (i) A will win all three games (ii) Two teams will win alternatively (iii) Two games will end up with a draw in each (iv) All three games will end up a draw in each. A second problem asks to analyze the marks distribution of students across two exams and find the probability of passing both. The third question is about expected petrol sales on rainy and clear days.

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Statistics
Expected Value

Formulas

P(A ∩ B) = P(A) * P(B) for independent events
Expected Value Formula: E(X) = Σ P(x) * x

Theorems

Law of Total Probability
Fundamental Counting Principle

Suitable Grade Level

Grades 11-12