# Conditional Probability

Conditional probability is a fundamental concept in probability theory, indispensable in various fields such as statistics, machine learning, and decision-making processes. It measures the likelihood of an event occurring given that another event has already happened. By expressing the probability of one event under the condition that another event has occurred, conditional probability enables precise modeling of uncertain scenarios. This notion plays a pivotal role in understanding dependencies between events and is extensively utilized in real-world applications ranging from risk assessment to medical diagnosis and beyond.

Questions

- A card is drawn from a shuffled deck of 52 cards, and not replaced. Then a second card is drawn. What is the probability that the second card is a king?
- A bag contains 4 red, 3 yellow and 2 purple discs. A disc is taken, at random, from the bag and is not replaced. A second disc is then taken, at random, from the bag. Calculate the probability that the two discs taken from the bag are different colours?
- Dr. Sox drives through two stoplights on her way to work. The first light is green for 20 seconds out of each minute. The second light is green for 35 seconds out of each minute. What is the probability that Dr. Sox will hit two green lights?
- The probability that rozaimah goes shopping is 0.8 on a sunny day and 0.4 on a rainy day. H forcefasted that it will rain tomorrow is 0.3. What is the probability that rozaimah will go shopping tomorrow?
- What is the meaning of conditional probability?
- How to solve extended response question using probability?
- #P(E)=.24# and #P(F)=.3#. What is #P(E uu F)#?
- 90 students will graduate from Lima Shawness High School this year. Out of the 90, 50 are planning to attend college. Two students are selected at to carry the flag at graduation. What is the probability that both of them are planning to attend college?
- How is Bayes' Theorem used to solve complex probability questions?
- In a two-child family, if one child is a boy, what is the probability that the other child is a girl? If the first child is a boy, what is the probability that the second is a girl?
- A card is drawn from a standard deck. A second card is drawn, without replacing the first card. Consider the following events: Event A = The first card selected is red. Event B = The second card selected is black. What word describes the relationship between events A and B?
- In a two child family, if one child is a boy, what is the probability that the other child is a girl? If the first child is a boy, what is the probability that the second is a girl?
- If you roll two die, what is the probability that the sum of the die rolls is 6? What is the probability that the sum is 6 if one die rolls a 4?
- Assume that A and B are events in a sample space and that P(A)=.40 and P(B/A) = .25. What is the probability that both A & B occur?
- Rob noticed that 55% of the people leaving the supermarket to chose plastic bags instead of paper bags. Out of 600 people how many can Rob predict will carry plastic bags?
- If the letters of the word Mississippi are placed in a hat, what is the probability that the first two letters drawn are both "i" if the first letter drawn is not replaced?
- Of 100 gumdrops 73 are large, 39 of them are red, and 19 are large and red. If you choose a random gumdrop, what is the probability that it is red? If the gumdrop is red, what is the probability that it is large?
- How does the General Multiplication rule differ from the Special Multiplication Rule of Probability?
- In hockey, Ed makes 7 goals for every 10 shots. If he takes 6 shots, what is the probability that he will make at least 5 goals?
- 3 balls are drawn from a jar that contains 5 white balls and 3 black balls. What is the probability that all 3 balls are same in color if there is no replacement?