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A square target board with a side length a = 12 cm is randomlyfired. What is the probability that the distance of the bullethitting the target from the center of th...

Question

A square target board with a side length a = 12 cm is randomlyfired. What is the probability that the distance of the bullethitting the target from the center of the square is less than d =4√3 cm?

A square target board with a side length a = 12 cm is randomly fired. What is the probability that the distance of the bullet hitting the target from the center of the square is less than d = 4√3 cm?



Answers

A, B, $C$ are three persons firing at a target. The probability that $A$ hits the target is $0.3$, for $B$ it is $0.4$ and for $C$ it is $0.5$. Probability that the target is hit, is (a) $1.2$ (b) $0.79$ (c) $0.6$ (d) $0.88$

But in this case we see that Bullets velocity reduces to half of its initial velocity when it penetrates to 60 cm. So we can write leaders wells to In its in its level Australia where there were two mm We can rate he divided to square. This will be calls to initially spirit square. Place to S. From here we get a Z equals two. We developed it to Holy Square. When is we square? The very way too as this will be negative. So it will be equal to It will be equals two -3 V Square. A little positive. Send. This will be called to -3 V sq provided by it is. Or let us substitute the value so minus three V squared divided by eight. Multiplied by S. Has given us 60 cm. So it is 0.6 m. So this will win meter per second square. So this is the acceleration, ordered the acceleration. No, no. We need to calculate further word distance. The bullet travels before coming tourists. So now we have finally speed we because 20 And in the sail straight via is equals to re divided by two and Excellence and is equals two minus tv square. The very best eight multiplied wear 60 the latest substitute the values here so we can write the final spirit. VF square minus initial spirit via is where this is a close to two A. S. So the final spirit is going to be zero Where it is zero sq minus initial. Speed is very, very were too square. This is a close to two multiplied with Excellence and his minus TVs where divided by eight, multiplied with sixties centimeter prepared with us. So upon solving we get distance table as Before coming to rest comes out to be 60 divided by three, which is equal to It is called to 20 cm The 20 cent interest, correct answer. And hence let's see options. The option number. He is correct.

Yeah that's probably we're told From a lot of 10 missiles. Three are selected at random. In fact. Now the lot contains four defective missiles as we have four defective. And so it's non effect mm. You know, hey we want to find the probability that the three that we choose are all working. Now. Those are six out of 10 chances. The first one we choose works since we've already chosen one of the ones that work. So probably the next one works is five out of nine. We have one less total and we have one less working. And then lastly the probably the last one works is four out of eight. For the same reason we have one less total and one less working. Okay. Multiply all these together will give us 16 and so there's a 16 chance that all of them work now on me. We want to find the probability that at most two will not fire. So the probability that the number of do not work Is less than or equal to two. This is equal to 1-. The probability that D. is equal to three. You'll notice that the total number we're choosing is equal to three and so there's less than equal to complement. That would be a 23 Which is 1-. And then we have four defective So they're probably the first is the effective is 4/10 Probability. The second is the fact was three nights And then to eight. So to get our probability we're going to multiply these together. Are we evaluate this. Mhm. Mhm. This gives us 29 out of 30.

This is all number 25. And visitors said that there is a fair inside cube. It is completely Fritz. Okay, if this is a cube, Okay. There is this fair inside it, which completely, which touches each side. He started each side of this cube. So now we have to find the probability that if we choose any point inside the cube inside the queue, it also becomes inside the sphere. So basically, we have to, uh, let us Ah, let us think like this. If we choose a point inside the Cube, including its periphery inside the story, if you choose any point inside the sphere inside the sphere, it will automatically come inside the cube. Also. So basically, we have to find the ratio off. Probability required relative will be the ratio off volume off the sphere. Divide the volume. Author Cuba. This will be very quiet Probability. So if we choose this to be our that is half length is are so complete length will be tour, So volume off sphere is always four by three by our Q divide by volume off Q to our cuba. So this will be four by three by our Q in tow. Eight R Q. Okay, so this will become by by six. So probability will be by by six. That is 22 by six into seven. That is 22 by 42 22. Divide by 42. That is open 5 to 38 0.5 to 38 So probability approximately will be 0.5 to 4. Thank you so much.

Problem. 13 Events You Want to See Too. C3 and C4 are independent events. Where each event represents a person that fires one shot at a target. The probabilities of these events are probability of Sichuan equals 0.7. The probability of C two Equals 4.7. The probability of C3 Equals 4.9 and the probability of C4 Equals 4.4. You want to compute the following probiotics. Yeah. All of them has it all. This means to get the probability of the intersection between the four events. As long as they are independent events, then we can get the multiplication of each event. Then assembly equals 0.7, multiplied by 0.7 deployed bio 0.9 Multiply it by 4.4 Equals 4.1764 for barbie, The probability of exactly one hits editor here we have four cases. The first kiss is see one or the first person heads target and the three others don't hit the target or the second one hit or the second The 3rd 1 hits or the 1st 1 had. This means we want to get the probability four C one intersect C. To complement the sick. This seat three compliment interceptors. See for complement this is the first scenario plus The probability for the second case or the second scenario that C1 miss the target, intercept C. Two that hits the target And History and C4 miss the top. No so you won't miss see to miss C. Three heads target. Ceo for miss the target and finally see you on misses the target. See to mrs see extremists & C4 hits in the dark Because C1 to C four are independent events then they're complement are also independent with the others. Then we can get the probability of the intersection by getting the probability or the multiplication of They're probably it's then it's a probability of someone Which is 0.7 multiplied by the probability of C to complement Which is 1 -0.7, gives 4.3 But deployed by 1 -0.9 Multiplied by 1- over in four plus one minus Open seven gives open three Multiplied by 1.7, deployed by 1 -4.9 multiplied by one or 0.4 plus. We only change this So .3 multiplied by open three and change this of course over. And three applied by open mine by by open six plus. We change this and this oh 0.3 multiplied by open three. Applied by a 30.1 supplied by 4.4. This gives 4.0126 plus 4.0126 plus four point oh 486 plus four point oh oh oh 36 Which gives as a final answer 4.0774. For part C. We want to find the probability that no one hits the target. No one has the target means the probability see one compliment all miss the target then see to complement Their sectors. c. three compliments C. Four compliment. We must deploy each of them Then it's 1 -0.7. give 0.3 Depoted by 1 -0.7. Multiplied by 1 0 nine But applied by 1 -20ine four. Give 0.6. Then the answer is 0.054. Finally for barney we want to find the probability at least one hits the target. Then we can find the probability of the compliment event Of no one it's a target. Then it's the probability of c. one compliment intersect C. To complement intersects the three complement intersects the four compliment old compliment, Then it's 1 -4.054. Then the answer is 4.9946. This is the probability That at least one hits the dark.


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