QUESTION NUMBER 2.31 ? I HOPE SOMEONE SOLVE IT BY STEPS Two boilers are used to
ID: 3173102 • Letter: Q
Question
QUESTION NUMBER 2.31 ?
I HOPE SOMEONE SOLVE IT BY STEPS
Two boilers are used to supply steam for the operation of a steam turbine. Each boiler can completely supply the steam to the turbine 80 percent of the time. The probability of failure of each boiler is 0.05 and that of both boilers failing simultaneously is 0.03.Find the probability of the steam turbine getting the complete supply of steam and one of the boilers failing simultaneously. Suppose that 15 percent of all people have a high -cholesterol level. It is found that 5 percent of people with a high-cholesterol level get a heart attack while only 1 percent of hose without a high-cholesterol level get heart attack. If a randomly selected person gets a heart attack, find the probability of that person having a high- cholesterol level Among the 30 students enrolled in an Engineering Design course, 23 belong to mechanical engineering branch and 7 belong to other branches of engineering. If 2 students are randomly chosen from this class, what is the probability of both the students belonging to a branch other than mechanical engineering? Suppose that 15 percent of all people have a high-cholesterol level. A particular type of cholesterol test, when used on a person having a high-cholesterol level, detects it correctly 95 percent of the time and fails to detect it 5 percent of the time. The same test, when used on a person without a high-cholesterol level, wrongly indicates a high-cholesterol level 4 percent of the time, (a) If the test shows a high-cholesterol level for a randomly selected person, what is the probability of that person actually not having a high-cholesterol level? (b) What is the probability of a randomly selected person having a high-cholesterol level and being indicated as such by the test? (c) What is the probability of a randomly selected person not having a high-cholesterol level but the test indicating the person as having a high-cholesterol level? (d) Do you consider the test to be reliable? A boiler has three independent safely valves which open and lei steam off to the atmosphere in case of a high-pressure buildup. The boiler is considered to be safe if at least two valves open in the ease of a high-pressure buildup. If the probability of each valve opening in case of high-pressure buildup is 0.9. find the probability of the boiler to be in the safe condition in case of a high-pressure buildup. A gear can fail due to either excessive bending stress or excessive surface wear. Let B and W denote the failures in these modes. If it is known that in a particular application, P(B) = 0.0005, P(W) = 0.001 and P(B)W) = 0.1, find(a) the probability of failure of the gear, and(b) The probability of a gear having only excessive bending stress excessive surface wear.Explanation / Answer
2.31 - The boiler is safe if any two valves are open or all 3 valves are open.
P(2 out of 3 valves will open) = 3 x 0.9 x0.9x0.1 = 0.243
P(all three valves will open) = 0.9x0.9x0.9 = 0.729
P(boiler to be in safe condition) = 0.243+0.729 = 0.972