Given:
A card is randomly drawn from a regular deck of cards and then replaced. A second card is then drawn.
Required:
Find the probability that the first card is a spade and the second one is the jack of clubs.
Explanation:
The total number of cards in the deck = 52
Total number of spade cards = 13
The total number of jack cards = 13
The number of jack club card = 1
The probability of an event is given by the formula:
[tex]P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]The probability that the first card is a spade is:
[tex]\begin{gathered} P(s)=\frac{13}{52} \\ P(s)=\frac{1}{4} \end{gathered}[/tex]A second card is drawn when the first card is replaced.
The probability that the second one is the jack of clubs:
[tex]P(c)=\frac{1}{52}[/tex]The probability that the first card is a spade and the second one is the jack of clubs:
[tex]\begin{gathered} P=P(s).P(c) \\ P=\frac{1}{4}\times\frac{1}{52} \\ P=\frac{1}{208} \end{gathered}[/tex]Final Answer:
Option a is the correct answer.F
