Probability

Question

Two cards are selected from a standard deck of 52 playing cards. The first is replaced before the second card is selected. Find the probability of selecting a spade and then selecting a king.

 

The probability that two events will occur in sequence is Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis times Upper P left parenthesis Upper B vertial line Upper A right parenthesisP(A and B)=P(A)•P(B|A).
If events A and B are? independent, then the rule can be simplified to Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis times Upper P left parenthesis Upper B right parenthesisP(A and B)=P(A)•P(B).
This simplified rule can be extended to any number of independent events. This is known as the Multiplication Rule for the probability of A and B.

 

Answer 1

probability of a spade: 13/52, or 1/4

probability of a king: 4/52, or 1/13

probability of a spade then a king: (1/4)(1/13), or 1/52