Probably That!

Probability Level 4

If on average 1 vessel in every 10 is wrecked, find the chance that out of 5 vessels expected 4 at least will arrive safely.

If the answer is a/b where a and b are co-primes then find a + b .

Note: its not as easy as you are thinking.


The answer is 95927.

Anand Raj by Anand Raj , 22, India

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1 solution

Benjamin Wong
Mar 4, 2014

Req. P.= P(4save)+P(5save)

P(4save)=5(0.1x0.9^4)

P(5save)=0.9^5

Therefore req. P. = 45927/50000

a+b=95927 QED

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you please be a bit more clear?

Krishna Ar - 7 years ago

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Probability that 4 ships come safely and 1 ship is sunk = ( 9 10 ) 4 × 1 / 10 = x (\frac{9}{10})^4 \times 1/10 = x . There are 5 ways for one ship to get sunk and the other 4 to come through, so the probability in this case = 5 x 5x .

Probability that all 5 ships come safely = ( 9 10 ) 5 = y (\frac{9}{10})^5= y .

x + y = 45927 50000 x + y = \frac{45927}{50000} .

45927 + 50000 = 95927 45927 + 50000 = \boxed{95927} .

Is that more clear?

Kartik Prabhu - 6 years, 11 months ago

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