Question

Two cards are drawn without replacement. What information do you need in order to calculate the probability that the second card is a red king, given that the first card is a black queen?The probability that the second card is a red kingThe probability of both a red king and a black queenThe probability that the first card is a black queenThe probability that the second card is a black queen aa and b ba and d cb and c dc and d

Answer 1

To explain properly this problem let's remember that the conditional probability of B given A can be calculated as:

`P(B|A)=P(A)P(A\cap B)`

In this case let A be the event "Drawing a black queen" and let B be the event "Drawing a red king"; with these definitions of events then we have that A∩B is the event "Drawing both a black queen and a red king". According to the formula above we need P(A) and P(A∩B), which means that we need:

• The probability that the first card is a black queen.

,

• The probability of both a red king and a black queen.

Therefore, we need to know b and c from the list given and the correct choice is option C.