Latest TCS Aptitude Question SOLUTION: the brobability of a bomb hiting a bridge is 1/2 and two direct hit are required to destroy it.the least no of bombrequired so that the probability of the bridge being destroyed i

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the brobability of a bomb hiting a bridge is 1/2 and two direct hit are required to destroy it.the least no of bombrequired so that the probability of the bridge being destroyed is greater than 0.9 is

Asked In TCS Amit sahu (10 years ago)

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ritabrata gautam  (10 years ago)

@ANAMIKA
probability of the bridge being destroyed is greater than 0.9 means
probability of the bridge being not destroyed is lesser than 0.1

now bridge is not destroyed in two cases 1 hit 0 hit
now let n bombs are needed now find all probabilities of the bridge being not destroyed by binomial distribution i.e.

[nC0+nC1]*(0.5)^n < 0.1

now examine it for values n=1,2,3,4,,....
you wil observe that for n = 1 to 6 the above inequality doesnt satisfy...it first time satisfies for n=7 ...now as least no. bombs are required said in que..so 7 will be the ans

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ritabrata gautam  (10 years ago)

7 is the correct answer
[nC0+nC1]*(0.1)^n < 0.1
now find when this relation is true (1st time) for n=2,3,4....
it will be 7

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Kundan Kumar  (10 years ago)

Probablility that bridge is not destroyed is 0.10
Hence
[nCo + nC1]*(1/2)^n

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LAXMI DURAI  (10 years ago)

plz explain it clearly...i cant get it

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ritabrata gautam  (10 years ago)

SORRY FOR THE TYPING MISTAKE ABOVE....

7 is the correct answer
[nC0+nC1]*(0.5)^n < 0.1
now find when this relation is true (1st time) for n=2,3,4....
it will be 7

Is this solution Helpfull? Yes (1) | No   

Yvaine  (10 years ago)

Suppose n = least number of bombs that must be dropped so that the probability of destruction of the bridge is greater than 0.99. Hence the probability that the bridge is NOT destroyed is less than 0.01.

If less than two bombs hit the bridge then it is not destroyed and probability of it is

[ nCo + nC1 ] ( 0.5 )^n < 0.01

=> ( 0.5 )^n < 0.01 / (n + 1)

Putting n = 1, 2, 3, and so on you find that inequality is not satisfied till n = 10 and is satisfied for n = 11.

when n = 10, LHS = 0.000976 < RHS = 0.000909 is false
when n = 11, LHS = 0.000488 < RHS = 0.000833 is true.

Therefore, n = 11.

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Ankur Raghuwanshi  (10 years ago)

ans. is 10...

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anamika  (10 years ago)

@ritabrata gautam- plz explain in bit detail...could nt get u..

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