Question

The probability that certain electronic component fails when first used is $0.10$. If it does not fail immediately, the probability that it lasts for one year is $0.99$. What is the probability that a new component will last for one year?

• A. $P\left(Y\right)=0.091$
• B. $P\left(Y\right)=0.891$
• C. $P\left(Y\right)=0.9$
• D. $P\left(Y\right)=0.99$

Answer 1

The correct option is B $P\left(Y\right)=0.891$

Probability that a new component lasts for one year$=$(probability that the component doesn't fail)$\times$(probability that it lasts for one year)$=(1-0.1)\left(0.99\right)=0.90\times 0.99=0.891$