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Homework in probability theory Variant 1 A box contains 15 red balls, 10 blue balls, and 5 white balls. 1. 2 balls are taken from the box. Consider the following events: A) the first ball is red B) the first ball is blue C) the first ball is white Find the following probabilities a) p(A)-? D) the second ball is red E) the second ball is blue F) the second ball is white b) p(B)? c) p(C)? d) p(D/A)- e) p(D/B)? f) p(D/C)-? 2. Find probabilities to take b) 2 blue balls c) one blue ball and one white ball a) 2 red balls We have taken 2 balls form the box. What are probabilities that we have taken a) at least one red bal b) at least one blue ball c) at least one white ball 3. 4. We have components manufactured by 3 different factories, 60% are manufactured by 1st factory, 30%-by 2nd factory, and 10%-by 3rd factory. 1st factory gives 0.5% of nonstandard components. 2nd factory-190, and 3rd factory-5%. We take one of these components. a) Find probability that component we have taken does not correspond to standards. Component really does not correspond to standards. Find probability that it is manufactured b) by Ist factory c) by 2nd factory d) by 3rd factory

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