# A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a diamond AND a king?choosing a diamond OR a king?please help me with my take home...

A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a diamond AND a king?choosing a diamond OR a king?

please help me with my take home quiz i need a detailed solutions thanks and Godbless !

embizze | Certified Educator

A single card is chosen from a deck of 52 cards.

(a) Find the probability of getting a diamond and a king.

The only card in the deck that is a diamond and a king is the king of diamonds. Thus the probability will be `1/52` .

P(A and B)=P(A)P(B)

The probability of getting a diamond is `13/52=1/4`

The probability of getting a king is `4/52=1/13`

P(diamond and king)=`1/4*1/13=1/52`

(b) Find the probability of getting a diamond or a king.

Here there are 13 diamonds and 4 kings. But we have counted the king of diamonds in both groups. Taking this into account there are 13+4-1=16 cards that meet the conditions. Thus there is a probability of `16/52=4/13` or getting a diamond or a king.

** Choosing a diamond and choosing a king are not mutually exclusive **

P(A or B)=P(A)+P(B)-P(A and B)

P(diamond)=`13/52=1/4`

P(king)=`4/52=1/13`

P(diamond and king)=`1/52` (calculated above.)

So P(diamond or king)=`1/4+1/13-1/52=13/52+4/52-1/52=16/52=4/13`