Engineering Mat...

An urn contains 5 red ball and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

5 cards are drawn from a pack of 52. What is the probability these five will contain just one ace?

If A, B and C are any 3 events such that \(P\left( A \right) = P\left( B \right) = P\left( C \right) = \frac{1}{4}\)

\(P\left( {A \cap B} \right) = P\left( {B \cap C} \right) = 0;\;\;P\left( {C \cap A} \right) = \frac{1}{8}\)

Find the probability that at least one of the events A, B and C occurs.

If A and B are two events such that P(A⋃B) = 5/6, P(A⋂B) = 1/3, P(B) = ½, then the events A and B are

A speaks truth 3 out of 4 times. There is a chance that match can be won, drawn or lost but A reported that Shyam has won the match. Find the probability that his report was correct.

A system throws 1, 3, and 5 errors for different applications in a day with an associated probability of \(\frac{1}{2},\frac{1}{3}\;and\;\frac{1}{6}\) of respectively. Find the mean and the variance of the errors thrown by a system in a day?

A bolt is manufactured by 3 machines A, B and C. A turns out twice as many items as B, and machines B and C produce equal number of items. 2% of bolts produced by A and B are defective and 4% of bolts produced by C are defective. All bolts are put into 1 stock pile and 1 is chosen from the pile. What is the probability that it is defective?

A unbiased coin is tossed three times and the outcome of the 1^st toss is head. The probability that a total of exactly two heads occur is ______

If a discrete random variable X has the following probability distribution

Evaluate the Standard deviation

Consider the following probability mass function (p.m.f.) of a random variable X:

\(p\left( {x,q} \right) = \left\{ {\begin{array}{*{20}{c}} q\\ {1 - q}\\ 0 \end{array}} \right.\begin{array}{*{20}{c}} {if\;X = 0}\\ {if\;X = 1}\\ {otherwise} \end{array}\)

If q = 0.4, the variance of X is___________.