probability

Introduction - Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life science..

Two major applications of probability theory in everyday life are in risk assessment and in trade on commodity markets. Governments typically apply probabilistic methods in environmental regulation where it is called "pathway analysis". Example: In a housing colony 70% of th..

Question and Answers 1 Question and Answers 1.1 Question and Answers 1.2 Question and Answers 1...

Two random experiments are said to be independent if for every pair of events E and F, where E is associated with the first experiment and F is associated with the second experiment, the probability of simultaneous occurrence of E and F, when the two experiments are performed, is the pro..

5 cards are drawn successively with replacement from well shuffled deck of 52 cards. What is the probability that i) all the five cards are spades ii) only 3 cards are spades iii) none is a spa..

In the probability distribution of ..

Introduction - Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a ..

A trial, which has only two outcomes i.e., "a success" or "a failure", is called a Bernoulli trial. Let X be the number of successes in a Bernoulli trial, then X can take 0 or 1 and P(X =1) = p = "probability of a success" P(X = 0) = 1 - p = q = "probability of failure". Conside..

a) The probability of drawing a white ball in the first draw is . Since the ball is replaced, the probability of getting white ball in the second draw is also . b) The probability of drawing a white ball in the first draw is . If the first ball drawn is white and..

In the previous section, we have learnt that i) If A and B are two mutually exclusive events, then ii) Before we state and prove Baye's Theorem, we use the above two rules to state the law of total probability. The law of total probability is useful in proving Baye's theorem and..