Answer :
Let A be the event that exactly one of the sampled tiles is defective.
In a batch of 17 tiles, 7 are defectives.
3 tiles are sampled at random.
3 tiles can b eselected from 17 tiles in
[tex]^{17}C_3=680[/tex]ways.
Therefore, the number of points in sample space is 680.
Now, 1 defective item can be selected from 7 defetctive items in 7 different ways. For each of these ways, remaining two items can be selected from (17-7)=10 non-defective items in
[tex]^{10}C_2=45[/tex]ways.
Therefore, from the batch of 17 tiles, 3 items can be selected so that exactly one item is defective in
[tex]45\times7=315[/tex]ways.
Therefore, total number of points in sample space in favour of the event A is 315.
By classical definition of probability,
[tex]\begin{gathered} P(A)=\frac{315}{680} \\ =\frac{63}{136} \end{gathered}[/tex]Hence, the probability that exactly 1 of the sampled tiles is defective is
[tex]\frac{63}{136}\approx0.46[/tex]