Practical Problems with Fundamental Probability Concepts
Abstract
In this class, we will review practical exercises such as the reliability of a control system, card game strategies, and probability calculations in everyday situations. The solutions to the problems are presented in video format, allowing you to strengthen your understanding and skills in the field of probability by comparing your developments and analyzing ours.
LEARNING OBJECTIVES:
By the end of this class, the student will be able to:
- Solve problems involving basic probability elements
At this point, it is necessary to do some practical exercises that involve the basic ideas of probabilities [1,2,3]. The advice, as always, is: first try to solve these probability exercises on your own, and then watch the video to compare and correct your results.
- A control system is made up of 10 components. The failure of any one of them can cause the entire system to fail. It is known that the probability of failure of each component is \leq 0.0002. Prove that the probability that the system will work correctly is \geq 0.998. [SOLUTION]
- On a table, there are three face-down cards: one “ace” and two “jokers”. The game consists of guessing which of the cards is an ace. You choose one and at that moment, the dealer shows you one of the other two cards, which turns out to be a “joker”, and gives you the opportunity to switch your choice. What is better: to keep or change your choice to the other unknown card? [SOLUTION]
- Case of an error in adding probabilities: [SOLUTION]
- Case 1: There are two baskets, one red and one white. The red basket has 5 gold coins and 6 tin coins, while the white one has 3 gold and 4 tin. From which basket is it more convenient to draw a coin?
- Case 2: Same as the previous case, there are two baskets, one red and one white. The red basket has 6 gold coins and 3 tin coins, while the white one has 9 gold and 5 tin. From which basket is it more convenient to draw a coin?
- Case 3: Now, the contents of the two previous red baskets are combined into one large red basket, and the same is done with the white baskets from the two previous cases. Will the trend observed in the previous cases hold?
- A store issues tickets with 5-digit numbers. If you draw a ticket at random, what is the probability that it will be a palindrome? NOTE: A palindrome is any number that reads the same backward as forward; for example: 13431 is a palindrome. [SOLUTION]
- A fair 6-sided die is rolled repeatedly. Calculate the probability of getting: [SOLUTION]
a) Two even numbers, rolling twice.
b) At least one ace rolling 4 times. - Five fair 6-sided dice are rolled. Calculate the probability of getting: [SOLUTION]
a) Five of the same number
b) Four of the same number and one different
c) Three of one number and two of another
Views: 0