Vikram wanted to find out how many moths there were in a small woodland.

One night, Vikram captured a random sample of 12 moths and marked them. He then released them back into the woodland.

The next night, Vikram captured a second random sample of 30 moths. He found that 9 of the moths in the second sample had been marked.

Vikram estimated that there were 40 moths in the woodland.

(a) Show that Vikram's estimate of the number of moths was correct.