Question

Consider a standard deck of 52 cards. You select one card at random and do not replace it. You shuffle the deck and then pick another card. If you are trying to find the probability that you pick a Red card first (denoted by R) and then a King card (denoted by K), which of the following probability statements is applicable for finding the probability?

P(R )P(K|R)

n(R AND K)/n(S)

P(R|K )P(K|R)

P(R )+P(K)-P(R n K)

Answer 1

In a deck of cards there are 52 cards . These 52 cards can be divided into four groups ( or suits ) ---- Hearts , Spades , Clubs and Diamonds. Spades and Clubs are black in color while Hearts and Diamonds are red in color . We have to find the probability that out of the two cards drawn the first card was a red card and the second card was a king card . Now each suit has a king card . Which means that two king cards are of red color . So , there is a possibility that a red king card is drawn . The possible scenarios that can arise in this situation is given below :

First card	Second card
R K	R K
R K	B K
R	R K
R	B K

R K means a red king card is drawn , B K means a black king card is drawn , R means a red card is drawn which is not a king card . So , here we have to find the value of the following expression :

This is the probability statement that is applicable in the current scenario.