Question

If you pick a card from a well shuffled deck, what is the probability that you get a face card or a spade?1/215/2611/261/13

Answer 1

Hello!

To solve this exercise, we must divide it into three possible cases:

• obtain a face card

,

• obtain a spade card

,

• obtain a face card from spades

First, let's remember that one deck hks 52 different cards, divided into 4 suits. Each suit has these cards:

• A, 2, 3, 4, 5, 6, 7, 8, 9, 10, ,J, Q, K,.

Knowing it, let's calculate some probabilities:

obtain a face card:

3 cards x 4 suits = 12 cards in a total of 52, so:

`(12)/(52)`

obtain a spade card

13 possible cards in a total of 52, so:

`(13)/(52)`

obtain a face card from spades

3 possible cards, in a total of 52.

Calculating the probability:

We must use the "or rule", which means to sum the result of the first condition with the result of the second condition. As these first two conditions cannot ocurr together, we have to subtract the third condition. Look:

`\begin{gathered} (12)/(52)+(13)/(52)=(25)/(52) \\ \\ (25)/(52)-(3)/(52)=(22)/(52)=(11)/(26) \\ \end{gathered}`

Answer:

Third alternative.

ha's reme