Problem #PRU-65777

Problems Probability and statistics Probability theory Conditional probability Discrete distribution Algebra Algebraic inequalities and systems of inequalities Linear inequalites and systems of inequalities Sequences Recurrent relations Linear recurrent relations
 14–16  4.0

Problem

A high rectangle of width 2 is open from above, and the L-shaped domino falls inside it in a random way (see the figure).

a) k L-shaped dominoes have fallen. Find the mathematical expectation of the height of the resulting polygon.

b) 7 G-shaped dominoes fell inside the rectangle. Find the probability that the resulting figure will have a height of 12.