The wording is somewhat ambiguous.Imsukhi wrote:Abhishek can kill a bird once in 3shots on the assumption that he fires 3shots. Find the probability that the bird is killed ?
a)1/3
b)19/27
c)8/9
Are we to assume that the person fires all three shots, even if he/she kills the bird on the first shot? Is it possible to shoot the bird more than once?
I'm assuming that we're asking, "If a person shoots at a bird exactly 3 times, what is the probability that he/she hits the bird at least once?".
If this is a proper rewording, then here's my solution:
When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(hitting the bird at least once) = 1 - P(not hitting the bird at least once)
What does it mean to not hit the bird at least once? It means missing all three times.
So, we can write: P(hitting the bird at least once) = 1 - P(missing all three times)
If the probability is 1/3 that the person hits the bird in one shot, then the probability is 2/3 that he/she misses.
So, P(missing all three times) = (2/3)(2/3)(2/3)
= 8/27
So, P(hitting the bird at least once) = 1 - 8/27
= 19/27
= B
Cheers,
Brent
