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Welcome to this lesson.
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In this lesson, we have a naval intelligence report that says that 10 enemy vessels in the fleet of 16 are carrying nuclear weapons.
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So here, if six vessels are randomly targeted and destroyed, we are looking at the probability that less than five vessels were less than five vessels were part of those that were destroyed.
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Carrying the nuclear weapons right so here we use the binomial probability to lose us and now we have four ability that we'll get a vessel that's carrying a nuclear weapon as 10 on 17 it means that the probability that the vessel is not carrying a nuclear weapon it's one minus 10 on 17 that is 7 on 17 so here using the binomial probability probability that x called to small x is equal to the n that is the sample size combination x then p to the par the probability of success to the power x then the probability of success to the power x then the probability of failure to the power n minus x okay so here we are looking at that less than five the vessels that were destroyed carrying nuclear weapons were less than five that means that they are between zero and four inclusive okay so less than five means zero one two three four okay but instead of doing for this which would be done for x call to zero escorts one up to 4 there's a shorter way of doing that course we can equally do from 5 to 6 or we can do from 5 to 6 5 and 6 then we subtract that from 1 and that would equally be the answer so here we know that if this is a binomial probability then if you do from 0 to 6 you would have 1 because the sample size is six so if you do for five and you do for six in addition the whole of this will give you one so we can move these two to join the one so that whatever we get would be the value from zero to four or less than five so probability that we'll get the vessels that we destroyed five of them less than five of them okay less than five of them were carrying the nuclear weapons this is equals to one then minus p x equals to four or the escorts to five then x equals to six right that is if we subtract x equals to five and x equal to six from both sides all right so this is equals to one minus for this one we using the formula here you have the n as six because we tag we use six uh they targeted six randomly so we have and that is called to six and that is six combination five probability of success which is 10 on 17 now this be to the par 5 the probability of failure which is 7 on 17 this would be to the power 1 and now this is minus when x -qualled to 6 we have 6 combination 6 okay then p which is 10 combinations 10 on 17 10 on 17 to the power 6 okay, x is 6, so to the power 6.
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Then now, probability of failure, which is 7, 117.
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Now, to the par, we have 6 here, so it should be 6 minus 6.
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That should be 0.
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All right, using this formula, n minus x...