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

MCQ

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?

A
$0.1542$
✓
$0.2647$
C
$0.3642$
D
$0.4231$

✓

Answer

Correct option: B.

$0.2647$

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.
Required probability $= P (A \cup B \cup C)$
$=1-P(\overline{A \cup B \cup C})$
$=1-P(\bar{A} \cap \bar{B} \cap \bar{C})$
$=1-P(\bar{A}) P(\bar{B}) P(\bar{C})[\because A, B, C$ 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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f\left( x \right) = \int\limits_x^{{x^2}} {\left( {t - 1} \right)\,dt\,\,,\,\,1 \le x \le 3,} $ then global maximum value of $f(x)$ is

Let $A = \{1, 2, 3\}.$ Then the number of relations containing $(1, 2)$ and $(1, 3),$ which are reflexive and symmetric but not transitive is:

The solution of the equation $\frac{{dy}}{{dx}} = \frac{{x + y}}{{x - y}}$ is

If $ a, b, c$ are the position vectors of three collinear points, then the existence of $x, y, z$ is such that

If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x ^{2}+\alpha x+\beta>0$, for all $x \in R$, is.

If for the matrix $A, A^3=1$, than $A^{-1}=$

If $y = {\tan ^{ - 1}}{{4x} \over {1 + 5{x^2}}} + {\tan ^{ - 1}}{{2 + 3x} \over {3 - 2x}}$, then ${{dy} \over {dx}} = $

Choose the correct answer from the given four options.

$\text{X}$	$1$	$2$	$3$	$4$
$\text{P}(\text{X})$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{3}{10}$	$\frac{2}{5}$

For the following probability distribution $E(X^2)$ is equal to:

If $y = \frac{{\sqrt[3]{{1 + 3x}}\sqrt[4]{{1 + 4x}}\sqrt[5]{{1 + 5x}}}}{{\sqrt[7]{{1 + 7x}}\sqrt[8]{{1 + 8x}}}}$ , then $y'(0)$ is equal to

The solution curve of the differential equation, $\left(1+ e ^{- x }\right)\left(1+ y ^{2}\right) \frac{ dy }{ dx }= y ^{2},$ which passes through the point $(0,1),$ is