A certain item is manufactured by machine M1 , and M2 . It is known that machine M1 turns out twice as many items as machine M2 . It is also known that 4 % of the items produced by machine M1 , and 3 % of the items produced by machine M2 are defective. All the items produced are put into one stock pile and then one item is selected at random. The probability that the selected item is defective is equal to

Question

A certain item is manufactured by machine M1 , and M2 . It is known that machine M1 turns out twice as many items as machine M2 . It is also known that 4 % of the items produced by machine M1 , and 3 % of the items produced by machine M2 are defective. All the items produced are put into one stock pile and then one item is selected at random. The probability that the selected item is defective is equal to (A)  (10/300)  (B)  (11/300)  (C)  (10/200)  (D)  (11/200)

Tardigrade Admin · Accepted Answer

Let number of item manufactured by machine

M_{1} = 200

According to the question, number of items manufactured by

M_{1}

is twice of number of item manufactured by machine

M_{2}

.

∴

Number of item manufactured by machine

M_{2} = \frac{200}{2} = 100

∴ 4%

of the items produced by machine

M_{1}

and

3%

of the items produced by machine

M_{2}

are defective.

∴

Number of defective items produced by machine

M_{1} = 200 \times 4% = 200 \times \frac{4}{100} = 8

and number of defective items produced by machine

M_{2} = 100 \times 3% = 100 \times \frac{3}{100} = 3

∴

Total number of items produced by machine

M_{1}

and

M_{2}

= 200 + 100 = 300

and total number of defective items produced by

M_{1}

and

M_{2}

= 8 + 3 = 11

∴

Probability that the selected item is defective

= \frac{Total number of defective items produced by machine M _{1} and M _{2}}{Total number of items produced by machine M _{1} and M _{2}}

= \frac{11}{300}

$\frac{10}{300}$

$\frac{11}{300}$

$\frac{10}{200}$

$\frac{11}{200}$

30010​

30011​

20010​

20011​

$\frac{10}{300}$

$\frac{11}{300}$

$\frac{10}{200}$

$\frac{11}{200}$