A factory has two machines, A and B

MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability

Problem

A factory has two machines, A and B. Machine A produces

60\%

of the total items, while machine B produces the remaining

40\%

. Of the items produced,

4\%

from machine A are defective and

5\%

from machine B are defective. Let

E

be the event that an item chosen at random is produced by machine A, and

F

be the event that the item is defective. (i) Calculate

P(E\cap F)

. (ii) Determine whether the events

E

and

F

are independent.