Probability Theory: Q1, Q2, and Q3

In summary, the conversation discusses probabilities related to drawing balls from an urn. Question 1 asks for the probability of the second lowest label from the balls drawn being m. Question 2 involves a game where two friends draw balls from an urn and the first player to get a white ball in the second draw wins. The probability of the first player not winning until the third draw is asked, given that they win. Finally, Question 3 deals with drawing balls from the urn and finding the probability of the m+n+2nd ball being white, given that the m+1st ball drawn was black.
  • #1
rishabhbhatt92
1
0
Q1. There are n cells and each cell contains k balls. One ball is taken from each of the cells. Find the probability that the second lowest label from the balls drawn is m.

Q2. Game played by two friends: each player picks two balls. The person who gets the first white ball in the second draw is the winner. Find the probability that the first player does not win till the third draw given that the first player wins. The urn from which they are drawing contains a white balls and b black
balls.

Q3. From an urn containing a white and b black balls first m balls are drawn one by one and then a ball is drawn. Then n balls are draw at one go and then another ball is drawn, then k more drawn. Given that the m+1 st ball is black find the probability that the m+n+2 nd ball is white.
 
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  • #2
Welcome to MHB! :D

Just for future reference, we ask that you post no more than two questions in a thread, and that you show what you've tried so our helpers can see where you may be going wrong and how best to help.

Keeping the number of questions down helps keep a thread from becoming convoluted and hard to follow, particularly if more than one person is trying to help with different problems at the same time.

These (and our other) rules are designed to make MHB as efficient as possible for everyone involved. (Yes)
 

Q1: What is probability theory?

Probability theory is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is used to quantify uncertainty and make predictions based on statistical data.

Q2: What are the main concepts of probability theory?

The main concepts of probability theory include sample space, events, probabilities, and random variables. Sample space is the set of all possible outcomes, events are subsets of the sample space, probabilities assign a numerical value to each event, and random variables are used to represent the outcomes of a random experiment.

Q3: How is probability calculated?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as P(A) = number of favorable outcomes / total number of outcomes. Probability can also be calculated using mathematical formulas and models such as the binomial distribution or the normal distribution.

Q4: What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or real-life events. It may differ from theoretical probability due to chance or other factors.

Q5: How is probability used in real life?

Probability theory has many practical applications in fields such as finance, insurance, and science. It can be used to analyze and predict outcomes in gambling and games of chance, to make decisions based on risk and uncertainty, and to model and understand complex systems and phenomena.

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