A string of decoration lights consists of 50 independent LED lights connected in

Question

A string of decoration lights consists of 50 independent LED lights connected in series with each other. The string of lights glow: if all the lights are good. The probability that an LED light is defective is 0.1. Find the probability that the string of lights glows. A manufacturer receives two boxes of resistors from a vendor. The first box contains 1,000 resistors of which 10% are defective. The second box contains 2,000 resistors of which 5% are defective. One box is selected at random and two resistors are tested and found good. Find the probability that the tested resistors came from box 2. A train and a passenger arrive at random and independently between 8: 0 am and 9: 0 am. The train makes a stop of 20 minutes. The passenger wants to board the train but he waits only to minutes and then leaves. Find t_0 so that the probability that the passenger wil board the train equals 0.5.

Explanation / Answer

P.1.8

This is a question of Binomial probability.

Given that the string of light glows if all the lights are good, which means there is no defective light or the number of defective lights is zero.

So the pdf of Binomial is -

P(x ; n,p) = nCx * px * (1 - p)n - x

where,

n = total number of lights

= 50

p = probability that a light is defective

= 0.1

x = number of success

= 0

So, P(x = 0) = 50C0 * (0.1)0 * (1 - 0.1)50 - 0

.   = 1 * 1 * 0.00515

.   = 0.00515

So, Probability that the string of light glows is 0.00515

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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