Question

A submarine fires n torpedoes in a row and all the firings are independent. Each torpedo hits the ship with the probability p and, in case of the hit, it damages randomly one of the k sections of the ship. The ship sinks if at least two sections are damaged. Find the probability that the ship will sink. 

          A submarine fires n torpedoes in a row and all the firings
are independent. Each torpedo hits the ship with the probability p
and, in case of the hit, it damages randomly one of the k sections
of the ship. The ship sinks if at least two sections are damaged.
Find the probability that the ship will sink.
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Added by Arthur M.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A submarine fires n torpedoes in a row and all the firings are independent. Each torpedo hits the ship with the probability p and, in case of the hit, it damages randomly one of the k sections of the ship. The ship sinks if at least two sections are damaged. Find the probability that the ship will sink.
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Transcript

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00:01 And this is a probable question and the p is the probability of hitting the ship.
00:05 So the p is the probability of hitting ship.
00:12 And what is the k? k is the number of ship here.
00:15 So the k is the number of.
00:20 So what we need? we need the probability of so i can just define the random variable x here.
00:26 So the random variable x, which is the number of times, which should be greater than 2.
00:32 So we can just use this as 1 minus the probability.
00:35 The excluded part less than or equal to one here.
00:39 So this is a binomial distribution, by the way...
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