Probability Tes...

On a multiple-choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

A manufacturer has three machine operators \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\). The first operator A produces \(1 \%\) defective items, whereas the other two operators \(B\) and \(C\) produce \(5 \%\) and \(7 \%\) defective items respectively. \(A\) is on the job for \(50 \%\) of the time, \(B\) is on the job for \(30 \%\) of the time and \(C\) is on the job for \(20 \%\) of the time. A defective item is produced, what is the probability that it was produced by A?

\(A , B\) and \(C\) are three mutually exclusive and exhaustive events. \(P ( A )=2 P ( B )=6 P ( C )\), Find \(P ( B )\):

Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are \(0.6\) and \(0.4\) respectively. Further, if the first group wins, the probability of introducing a new product is \(0.7\) and the corresponding probability is \(0.3\) if the second group wins. Find the probability that the new product introduced was by the second group.

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale:

An urn contains 5 red and 5 black balls. A ball is drawn at random, its color is noted, and is returned to the urn. Moreover, 2 additional balls of the color drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

Suppose a girl throws a die. If she gets a 5 or 6 , she tosses a coin three times and notes the number of heads. If she gets \(1,2,3\) or 4 , she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw \(1,2,3\) or 4 with the die?

\(60 \%\) of the employees of a company are college graduates. Of these, \(10 \%\) are in sales. Of the employees who did not graduate from college, \(80 \%\) are in sales. The probability that an employee selected at random is in sales is:

Assume that the chances of a patient having a heart attack are \(40 \%\). It is also assumed that a meditation and yoga course reduce the risk of heart attack by \(30 \%\) and prescription of certain drug reduces its chances by \(25 \%\). At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.