Question

The probability of being dealt a club and a diamond is

Answer 1

There are a total of 52 cards in a standard deck.

There are 13 club cards and 13 diamond cards.

The probability of getting a club card is given by

`P(club)=\frac{\text{number of club cards}}{\text{total number of cards}}=(13)/(52)`

The probability of getting a diamond card is given by

`P(diamond)=\frac{\text{number of diamond cards}}{\text{total number of cards}}=(13)/(52)`

The probability of getting a club and diamond is given by

"And" means to multiply the probabilites

`\begin{gathered} P(club\; \; and\; \; diamond)=P(club)* P(diamond) \\ P(club\; \; and\; \; diamond)=(13)/(52)*(13)/(52) \\ P(club\; \; and\; \; diamond)=(169)/(2704)=(1)/(16) \end{gathered}`

Therefore, the probability of getting a club and diamond is 1/16