Consider f(x)=x3+ax2+bx+c. Parameters a, b, c are chosen, respectively, by throwing a die three times. Then the probability that f(x) is an increasing function is
In a relay race there are five teams A. B, C. D and E.(a) What is the probability that A. B and C finish first, second and third, respectively.(b) What is the probability that A. B and C are first three to finish (in any order) (Assume that all finishing orders are equally likely).
Let A ,B ,C be three events. If the probability of occurring exactly one event out of A and B is 1−x, out of B and C is 1−2x, out of C and A is 1−x and that of occurring three events simultaneously is x2 , then prove that the probability that at least one out of A, B, C will occur is greater than 1/2 .
Assume that the chances of a patient having a heart attack is 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?
The unbiased dice is tossed until a number greater than 4 appear. What is the probability that an even number of tosses is needed?
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:S.No. Name Sex Age in years1. Harish M 302. Rohan M 333. Sheetal F 464. Alis F 285. Salim M 41A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
Consider a sample space S representing the adults in a small town who have completed the requirements for a college degree. They have been categorized according to sex and employment as follows: , Employed, Unemployed Male, 460, 40 Female, 140, 260 An employed person is selected at random. Find the probability that the chosen one is a male.
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?