Question

An instrument consists of two units. Each unit must function for the instrument to operate. The reliability of the first unit is $0.9$ & that of the second unit is $0.8$. The instrument is tested & fails. The probability that "only the first unit failed & the second unit is sound" is?

• A. $1/7$
• B. $2/7$
• C. $3/7$
• D. $4/7$

Answer 1

The correct option is B $2/7$

The reliability of first unit is $0.9$ and second unit is $0.8$

So,

$P\left(I\right)=0.9$

$\overline{P}\left(I\right)=1-0.9=0.1$

$P\left(II\right)=0.8$

$\overline{P}\left(II\right)=1-/08=0.2$

Reliability of $I$ failing and II sound

$=0.1\times 0.8=0.08$

$I$ sound and $II$ failing $=0.1\times 0.2=0.02$

The probability of first unit failing and second unit sound is:

$\frac{0.8}{0.08+0.18+0.02}$

$=\frac{0.08}{0.28}$

$=\frac{4}{14}$

$=\frac{2}{7}$