# Applied Mathematics for Electrical Engineering(3130908)

BE | Semester 3  Unit : Basic Probability

## Q3 (a) Winter-2019   Define the following. Favorable event Random variable Probability density function

Unit : Basic Probability

## Q3 (b) Winter-2019   An urn contains 10 white and 3 black balls, while another urn contains 3 white and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the later. What is the probability that it is a white ball?

Unit : Basic Probability

## Q3 (c ( i )) Winter-2019   In producing screws, let A mean “screw too slim” and B “screw too small”. Let $\mathrm{P}\left(\mathrm{A}\right)=0.1$ and let the conditional probability that a slim screw is also too small be $\mathrm{P}\left(\mathrm{B}/\mathrm{A}\right)=0.2$. What is the probability that the screw that we pick randomly from a lot produced will be both too slim and too short?

Unit : Basic Probability

## Q3 (c ( ii )) Winter-2019   The joint probability density function of two random variables $\mathrm{x}$ and $\mathrm{y}$ is given by . Find the marginal density function of $\mathrm{x}$ and $\mathrm{y}$.

Unit : Basic Probability

## Q4 (a) Winter-2019   Define the following. Mutually exclusive events Probability Compound events

Unit : Basic Probability

## Q4 (b) Winter-2019   State Bayes’ theorem. In a bolt factory, three machines A, B, and C manufacture 25%, 35%, and 40% of the total product respectively. Out Of these outputs 5%, 4%, and 2% respectively are defective bolts. A bolt is picked up at random and found to be defective. What are the Probabilities that it was manufactured by machines A, B, and C?

Unit : Basic Probability

## Q4 (c ( i )) Winter-2019   A person is known to hit the target in 3 out of 4 shots, whereas another person is known to hit the target in 2 out of 3 shots. Find the probability of the target being hit at all when they both try.

Unit : Basic Probability

## Q4 (c ( ii )) Winter-2019   Out of five cars two have tyre problems and one has break problem and two are in good running condition. Two cars are required for the journey. If two cars are selected among five at random and if X denotes the number with tyre problem, Y denotes with break problem then find the marginal probability function of X and Y.

Unit : Basic Probability