A thermal plant buys four boilers. If there is a 50% chance that each boiler wor

Question

A thermal plant buys four boilers. If there is a 50% chance that each boiler works for a year without any breakdown. (G: Event: Boiler is good and B: Event boiler is bad) 2.1 Identify possible events at the end of the year in tabular form showing condition of each boiler and total number of boilers in good condition at the end of the year. 2.2 Draw a sample space (Venn Diagram) corresponding to the state of boilers at end of year. 2.3 Find (1) probability of having one boiler left operative at end of first year and (2) probability of having at least 3 boilers at the end of first year.

Explanation / Answer

a and b) posible conditions

G,G 0.25

G,B 0.25

B,G 0.25

G,G 0.25

boilers in good condition = good, good = 0.25

Now there are 4 boilers , total in good condition are 4*0.25 = 1

c) probaility of one boiler operative at end of year

(b,g ) (g,b) = 0.50

d) prob of having at least 3 boilers = 1 - 0.25 = 0.75

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