Statistics

An urn contains \(4\) black balls and \(6\) white balls. What is the probability of getting \(1\) black and \(1\) white ball in two consecutive draws from the urn?

From a bag containing \(4\) black balls and \(5\) white balls, two balls are drawn one at a time. Find the probability that one ball is white and one ball is black. Assume that the first ball is returned before the second ball is drawn.

If 15% of the bolts produced by a machine are defective, determine the probability that out of 5 bolts chosen at random, at most 2 bolts will be defective.

From past experience, it is known that 90 percent of one-year-old children can distinguish their mother’s voice from a similar sounding female. A random sample of 20 one-year-olds is given this voice recognition test. Find the standard deviation of the number of children who recognize their mother’s voice.

A school has 5 divisions in class IX having 60, 50, 55, 62 and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is the overall average of the marks per student?

The probability that a randomly chosen sales prospect will make a purchase is 0.18. If a salesman calls on 5 prospects, what is the probability that the salesman will make exactly 3 sales?