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Chapter 5: Q 89. (page 331)

Bright lights? A string of Christmas lights contains 20 lights. The lights are wired in series so that if any light fails the whole string will go dark. Each light

has a probability0.02 of failing during a3-year period. The lights fail independently of each other. Find the probability that the string of lights will remain bright for 3 years.

Short Answer

Expert verified

P (20 lights not fail) =66.76%

Step by step solution

01

Step 1. Given Information

There are 20lights in a string of Christmas lights. The lights are connected in series, with a 0.02 chance of failure during a three-year period.

02

Step 2. Concept used

Multiplication rule: P(A鈭�B)=P(A鈭�B)脳P(B/A)

Complement rule:P(notA)=1鈭�P(A)

03

Step 3. Calculation

P(fail)=0.02

Complement rule to use:

P(notA)=1鈭�P(fail)=1鈭�0.02=0.08

Use the following multiplication rule:

P(A鈭�B)=P(A)脳P(B)

P(20lightsnotfail)=(P(fail))20=(0.98)20鈮�0.6676=66.76%

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