A machine operates if all of its three components function. The p… - Vidyadip

Question

A machine operates if all of its three components function. The probability that the first component fails during the year is $0.14$ , the second component fails is $0.10$ and the third component fails is $0.05$ . What is the probability that the machine will fail during the year?

✓

Answer

$(b) :$ Consider the following events:
$A=$ First component of the machine fails during the year
$B=$ Second component of the machine fails during the year
$C=$ Third component of the machine fails during the year
We have, $P(A)=0.14, P(B)=0.10$ and $P(C)=0.05$
Clearly, the machine will fail if at least one of its three components fails during the year.
$\text { Required probability }= P (A \cup B \cup C)$
$=1-P(\overline{A \cup B \cup C})=1-P(\bar{A} \cap \bar{B} \cap \bar{C})$
$=1-P(\bar{A}) P(\bar{B}) P(\bar{C})[\because A, B, C \text { are independent events }]$
$=1-(1-0.14)(1-0.10)(1-0.05)$
$=1-(0.86)(0.90)(0.95)=0.2647 .$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

In a binomial distribution, the probability of getting success is $\frac{1}{4}$ and standard deviation is 3. Then, its mean is:

If $\alpha=\tan^{-1}\Big(\tan\frac{5\pi}{4}\Big)$ and $\beta=\tan^{-1}\Big(-\tan\frac{2\pi}{3}\Big),$ then:

$4\alpha=3\beta$
$3\alpha=4\beta$
$\alpha-\beta=\frac{7\pi}{12}$
$\text{none of these}$

The point$(s),$ at which the function $f$ given by $f(x)=\left\{\begin{array}{l}\frac{x}{|x|}, x<0 \\ -1, x \geq 0\end{array}\right.$ is continuous, is$/$are

If the tangent to the curve $x = at^2, y = 2$ at is perpendicular to $x-$axis, then its point of contact is:

Let $g ( x )=\left\{\begin{array}{ll}e^{2 x}, & x<0 \\ e^{-2 x}, & x \geq 0\end{array}\right.$ then $g ( x )$ does not satisfy the condition

Let $f(x) = x^3 -6x^2 +15x + 3.$ Then:

If $d$ is the determinant of a square matrix $A$ of order $n,$ then the determinant of its adjoint is$:$

The function $f : R \rightarrow R, f(x) = x^2$ is:

In which of the following intervals is $y=x^2 e^{-x}$ increasing ?

If $\text{A} = \begin{bmatrix}1&\text{amp; } \log_{\text{b}}\text{a}\\ \log_\text{a}\text{b}&\text{amp; } 1\end{bmatrix}$then $ |\text{A}|$ is equal to:

$0$
$\log_\text{a}\text{b}$
$-1$
$\log_\text{b}\text{a}$