Respuesta :
SOLUTION:
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)
[tex]\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}}\times\frac{n(diamonds)}{\text{Total}} \\ Pr\text{ = }\frac{4}{52}\times\frac{13}{52} \\ Pr=\text{ }\frac{52}{52\times52} \\ Pr=\text{ }\frac{1}{52}\text{ } \end{gathered}[/tex]Final answer:
The probability of taking a 9 and then a diamond with replacement is:
[tex]Pr=\text{ }\frac{1}{52}\text{ }[/tex]