Solution:

Let E1 represent the probability that the drawn card is a diamond, E2 represent the probability that the drawn card is not a diamond, and represent the probability that the card is lost.

As we all know, there are 13 diamond cards and 39 non-diamond cards in a deck of 52 cards.

Then and

When a diamond card is lost, there are now 12 diamond cards remaining out of a total of 51. In ways, two diamond cards can be selected from a deck of 12 diamond cards.

In the same way, two diamond cards can be picked from a total of 51 cards in ways.

When one diamond card is lost, the chance of obtaining two cards is .

Also

Also

When no diamond card is lost, there are 13 diamond cards remaining out of a total of 51.

In ways, two diamond cards can be selected from a deck of 13 diamond cards.

In the same way, two diamond cards can be picked from a total of 51 cards in ways.

When a non-diamond card is lost, the probability of obtaining two cards is .

.

Also

Given that the card is lost, the probability that the lost card is diamond is .

Using Bayes’ theorem, we may deduce:

We may now retrieve the result by swapping the values.