Question

Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a diamond for the second card drawn, if the first card, drawn with replacement, was a club? Express your answer as a fraction or a decimal rounded to four decimal places

Answer 1

Given:

Two cards are drawn without replacement from a standard deck of 52 playing cards.

Required:

Find the probability of choosing a diamond for the second card drawn, if the first card, drawn with replacement, was a club.

Step-by-step explanation:

The total number of cards in the deck = 52

The number of diamonds cards = 13

The number of club cards = 13

The probability of an event is given by the formula:

`P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}`

The probability that the first card is a club:

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

If the drawn first card is not replaced then the left card is = 51

The probability that the second card is a diamond :

`=(13)/(51)`

Now the probability of choosing two cards, if the first is a club and the second is a diamond:

`\begin{gathered} =(1)/(4)*(13)/(51) \\ =(13)/(204) \\ =0.0637 \end{gathered}`

Final answer:

The required answer is 0.0637.