Question

You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a ninethe first time and a diamond the second time.

Answer 1

Case: A deck of cards (Probability)

A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. There are 52 cards in the deck.

Given:

A case of replacement. Picking a 9 on the first draw and a diamond on the second draw

Required: To find the probability of picking a 9 on the first draw and a diamond on the second draw

Method:

Total number of cards: 52

Number of 9's = 4 (From the four different suites)

Number of diamonds= 13 (From each suites)

`\begin{gathered} A\text{ case with replacement} \\ \text{Taking a 9 first and then taking a diamond} \\ Pr(9\text{ and 'Diamond')} \\ Pr\text{ = }\frac{n(9)}{\text{Total}}*\frac{n(diamonds)}{\text{Total}} \\ Pr\text{ = }(4)/(52)*(13)/(52) \\ Pr=\text{ }(52)/(52*52) \\ Pr=\text{ }(1)/(52)\text{ } \end{gathered}`

Final answer:

The probability of taking a 9 and then a diamond with replacement is:

`Pr=\text{ }(1)/(52)\text{ }`