
An article manufactured by a company consists of two parts $X$and $Y$.In the process of manufacture of the part$X$, $9$ out of $100$parts may be defective. Similarly $5$out of $100$are likely to be defective in part $Y$.Calculate the probability that the assembled product will not be defective.
Answer
513.6k+ views
Hint: Equate the part X that is not defective to a variable and do the same thing with Y as well and then find the intersection of the two cases.
Let $A = Part X$ is not defective.
Probability of $A$ is $P\left( A \right) = \dfrac{{91}}{{100}}$
Similarly for $B$,
$B = Part Y $is not defective
Probability of $B$ is $P\left( B \right) = \dfrac{{95}}{{100}}$
Required Probability is,
$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$
$P\left( {A \cap B} \right) = \dfrac{{91}}{{100}} \times \dfrac{{95}}{{100}}$
$P\left( {A \cap B} \right) = \dfrac{{8645}}{{10000}}$
Note: We took 2 variables A and B as the non defective ones and then found the probability by taking the intersection of these 2 cases.
Let $A = Part X$ is not defective.
Probability of $A$ is $P\left( A \right) = \dfrac{{91}}{{100}}$
Similarly for $B$,
$B = Part Y $is not defective
Probability of $B$ is $P\left( B \right) = \dfrac{{95}}{{100}}$
Required Probability is,
$P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right)$
$P\left( {A \cap B} \right) = \dfrac{{91}}{{100}} \times \dfrac{{95}}{{100}}$
$P\left( {A \cap B} \right) = \dfrac{{8645}}{{10000}}$
Note: We took 2 variables A and B as the non defective ones and then found the probability by taking the intersection of these 2 cases.
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

Write an application to the principal requesting five class 10 english CBSE
