Question

You are choosing two cards, replacing the first card in the deck, after it has been drawn? What is the probability you choose two consecutive diamonds?

Answer 1

To find a probability, divide the number of favorable outcomes by the total number of possible outcomes.

Since the number of cards in a deck is 52, it follows that the total number of possible outcomes is 52.

The number of diamonds in a deck of 52 cards is 13. Hence, the number of favorable outcomes is 13.

Since the first card is replaced, there'll be no alteration in the number of cards.

The first probability is:

`(13)/(52)`

The second probability is:

`(13)/(52)`

Hence, the probability of choosing two consecutive diamonds, replacing the first card is:

`\begin{gathered} (13)/(52)*(13)/(52) \\ =(1)/(4)*(1)/(4) \\ =(1)/(16) \end{gathered}`