Question

A card is randomly drawn from a regular deck of cards and then replaced. A second card is thendrawn. Determine the probability that the first card is a spade and the second one is the jack ofclubs.a. 1 out of 208b. 1 out of 56c. 1 out of 204d. 1 out of 55

Answer 1

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.

Step-by-step 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:

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

The probability that the first card is a spade is:

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

A second card is drawn when the first card is replaced.

The probability that the second one is the jack of clubs:

`P(c)=(1)/(52)`

The probability that the first card is a spade and the second one is the jack of clubs:

`\begin{gathered} P=P(s).P(c) \\ P=(1)/(4)*(1)/(52) \\ P=(1)/(208) \end{gathered}`

Final Answer:

Option a is the correct answer.F