3. (ust TRYthese and show work. Talk about them with others!) Assume the probabl

Question

3. (ust TRYthese and show work. Talk about them with others!) Assume the probablity that a missile hits a target from long range is 0.30. Assume the firing and aiming of all missiles is independent of every other missile. 5 missiles are fired. What is the probability of (show wor)... a. The first missile hitting the target b. All of them hitting the target c. None of them hitting the target d. The first missile that hits the target is the fourth target? e. At least one of them hitting the target? f, *"How many missiles would you need to fire in order to have at least a 90% probability of hitting the target? Tricky e This is tough. Logarithms work well here (though not required).

Explanation / Answer

a)P(fist misle hit the target)=0.30

b) P(all of them hit the target) =P(first hit and second and third and fourth and fifth hit)=(0.30)5 =0.00243

c)

P(none of them hit the target)=(1-0.3)5 =0.16807

d)

P(first hit is on fourth missile) =P(first 3 missle do not hit and 4th hit) =(0.7)3*0.3=0.1029

e)

P(at least one hit) =1-P(none hit )=1-0.16807 =0.83193

f)let number of missile required =n

P(at least one hit)=1-(none hit) =1-(0.7)n >=0.9

n>=ln(0.1)/ln(0.7)

n>=6.45

hence numebr of missile required =7

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.