(a) Three mathematicians are trying to decipher a coded document. If the probabi

Question

(a) Three mathematicians are trying to decipher a coded document. If the probability of each of them successfully deciphering the document is 1/3 , 1/5 , 1/4 respectively, and the three people work independently from each other, what is the probability that the document will be deciphered?

(b) A new light bulb has a probability of 3/4 of remain working after 1500 hours, and a probability of 1/2 of remain working after 2000 hours. A particular light bulb has been used for 1500 hours and is still working. What is the probability that this light bulb can be used for another 500 hours at least?

Explanation / Answer

(A)

The document will be deciphered if at least one of three mathematicians decipher the docoment.

Let M1 shows the event that first mathematicians decipher the code, M2 shows the event that second mathematicians decipher the code and M3 shows the event that third mathematicians decipher the code.

So we have

P(M1) = 1/3, P(M2) = 1/5, P(M3) = 1/4

By the complement rule we have:

P(not M1) =1 - P(M1) = 2/3, P(not M2) =1 - P(M2) = 4/5, P(not M3) = 1 - P(M3) = 3/4

SO the probability that none of them will able to decipher the code is

P(not all able to decipher the code) = P(not M2) P(not M2) P(not M3) =(2/3)*(4/5)*(3/4) = 0.4

By the cmplement rule, the probability that the document will be deciphered is

P(deciphered) = 1 - P(not all able to decipher the code) = 0.6

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