Question

You have a standard deck of playing cards from which you randomly select a card. Event D is getting a diamond and Event F is getting a face card (jack, queen, or king). What is the probability that a face card selected is a diamond?

Answer 1

We randomly select one card from 52, so there are 52 outcomes and:


`\overline{\overline{\Omega}}=52`

We also know, that there are
`4\cdot3=12` face cards in a standard deck (
`\overline{\overline{F}}=12`) and only three of them are diamonds, so


`\overline{\overline{D\cap F}}=3`

With this informations, we can calculate our probability:


`P\left(D|F\right)=(P\left(D\cap F\right))/(P(F))=((3)/(52))/((12)/(52))=(3\cdot52)/(52\cdot12)=(3)/(12)=\boxed{(1)/(4)}`