First problem: There are 10 members of the management board of a company. They choose the "leaders" of the company - a president, a vice president and a secretary. Find the probability out of 3 members of the management board:
a)3 of them to be hired as leaders;
b)none of them to be hired as leaders;
c)2 of them to be hired as leaders;
d)maximum 2 of them to be hired as leaders.
Second problem: A machine consists of two elements. The operation of each element is unconditionally needed for the operation of the machine. The probability of a flawless operation, during the period of time T, for the first element is - 0.8 and for the second - 0.9. The machine is tested for a period of time T. The results show that the machine has stopped operating. Find the probability only the first element to have broken(stopped working) while the second one has worked flawlessly during the test.
Third problem: An electrical applience works in two modes - lightly loaded and heavily loaded. The applience is lightly loaded for 7 hours and heavily loaded for 17 hours in the period of 24 hours. The probability the applience to break when it's lightly loaded is 0.001 and while heavily loaded - 0.01. Determine the reliability of the applience during a period of 24 hours.
a)3 of them to be hired as leaders;
b)none of them to be hired as leaders;
c)2 of them to be hired as leaders;
d)maximum 2 of them to be hired as leaders.
Second problem: A machine consists of two elements. The operation of each element is unconditionally needed for the operation of the machine. The probability of a flawless operation, during the period of time T, for the first element is - 0.8 and for the second - 0.9. The machine is tested for a period of time T. The results show that the machine has stopped operating. Find the probability only the first element to have broken(stopped working) while the second one has worked flawlessly during the test.
Third problem: An electrical applience works in two modes - lightly loaded and heavily loaded. The applience is lightly loaded for 7 hours and heavily loaded for 17 hours in the period of 24 hours. The probability the applience to break when it's lightly loaded is 0.001 and while heavily loaded - 0.01. Determine the reliability of the applience during a period of 24 hours.