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:

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