Mathematics - Probability Question with Solution | TestHub

Probability that the electronic component fails when first used is $P(F)=0.10$. Therefore, $P\left(F^{\prime }\right)=1-P(F)=0.90$ Let $E$ be the event that a new component will last for one year. $\text{ Then, }P(E)=P(F)P\left(\frac{E}{F}\right)+P\left(F^{\prime }\right)P\left(\frac{E}{F^{\prime }}\right)$ [total probability theorem] $=0.10\times 0+0.90\times 0.99=0.891$