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?
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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 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`