Casework and Law of Total Probability
Read this topicExplanations 4
- The law of total probability is a rule allowing us to compute the probability of an outcome that can be achieved through multiple different events. For example, suppose we have …
By Moor Xu, Victor Wang, Ruiran Xun, Joshua Siktar
- The Law of Total Probability Before diving into this topic, consider the following scenario. There is a nation called ExpiiLand this country is made up of four provinces. ExLand…
By Victoria Rodriguez, Joshua Siktar, Alex Federspiel
- Casework Casework is the method of solving probability problems by considering the different cases of a particular problem and adding them together. Casework is not the most gla…
By Sarah Walker, Joshua Siktar
- (Video) Law of Total Probability Problem 1 by Tutorials Point In this video, we walkthrough a problem involving the law of total probability. Summary\large{\text{Summary}}Summar…
By Amy Feraco
Problems 21
- Two dice appear to be standard dice with their faces numbered from 111 to 666, but each die is weighted so that the probability of rolling the number kkk is directly proportiona…
- Suppose two factories each make cell phones. Factory A makes 65%65\%65% of the cell phones on the market and Factory B makes 35%35\%35% of the cell phones on the market. 15%15\%…
- If you choose a piece of candy randomly from a random bowl, what are the chances of picking a chocolate candy? (Round to the nearest whole percentage.)
- Consider the following: 75%75\%75% of people exercise regularly. Of that 75%75\%75%, only 50%50\%50% have a gym membership. 20%20\%20% of the people who do not exercise regularl…
- Consider the following: A soccer team scores first 65%65\%65% of their games. The soccer team wins 60%60\%60% of the time when it scores first. The soccer team also wins 10%10\%…
- A shoe store orders all of its shoes from two factories. Factory A makes 47%47\%47% of the shoes sold at the shoe store. Factory B makes 53%53\%53% of the shoes sold at the shoe…
- In which of the following scenarios does the law of total probability apply? (Select all that apply)
- Which of the following is the correct notation for the law of total probability?
- How many three-digit numbers exist such that the last digit is the sum of the first and second digits?
- You have two buckets, each containing red and blue balls. Bucket A has 888 red balls and 121212 blue balls. Bucket B has 212121 red balls and 999 blue balls. If you randomly cho…
- How many three digit numbers have exactly 222 different digits?
- On any given day, what is the overall probability of you having to wait in line for over 101010 minutes?
- After 333 steps, what is the probability of the ant being at the point 222?
- You are on the illustrious Pittsburgh Riverotters soccer team. Whenever the Riverotters score the first goal, there is a 757575% chance they will win the game. If the opposing t…
- You are a car salesman and want to add new vehicles to your lot. There are 333 styles of vehicles to pick from: hot rod, truck, and van. Hot rods will be chosen with a probabili…
- Let's say we have two separate buckets of balls, a red bucket and a blue bucket. The red bucket has 555 red balls (but nothing else), while the blue bucket has 888 blue balls (b…
- In a certain state: 606060% of people like dogs (dog-lovers), 303030% like cats (cat-lovers), and 101010% do not like either (haters). When these people were asked if they liked…
- If there are 525252 cards in a deck, and there are 444 aces, what are the chances the second card you pick is an ace?
- We have 333 boxes of batteries. The number of good and dead batteries in each box are as follows: Box 111: 333 good, 222 dead Box 222: 444 good, 111 dead Box 333: 222 good, 222 …
- True or False: The law of total probability is used when you know the probability of an event.
- You have the graph of y=∣x∣y = |x|y=∣x∣ and decide to make another graph, for a function z,z,z, where you randomly do a horizontal translation of yyy of size −1,0,-1, 0,−1,0, or…