Math Problem Statement

A multiple-choice test consists of 8 questions with 3 answers to each question (of which only one is correct). A student answers each question by rolling a balanced die and checking the first answer if he gets 1 or 2, the second answer if he gets 3 or 4 and the third answer if he gets 5 or 6. To get a distinction, the student must secure at least 75% correct answers. If there is no negative marking, what is the probability that the student secures a distinction?

b.

In a book of 520 pages, 390 typo-graphical errors occur. Considered Poisson law for the number of errors per page, find tile probability that a random sample of 5 pages will contain no error.

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Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Poisson Distribution

Formulas

Binomial probability formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Poisson probability formula: P(Y = k) = (e^(-λ) * λ^k) / k!

Theorems

Binomial theorem
Poisson theorem

Suitable Grade Level

Grades 11-12