Question

Two cards are drawn from a well shuffled pack of 52 playing cards one by one without replacement. If $A$ : the event that the second card drawn is an ace and B : the event that the first card drawn is an ace card. then which of the following is true?

• A. $P ( A )=\frac{4}{17} ; P ( B )=\frac{1}{13}$
• B. $P ( A )=\frac{1}{13} ; P ( B )=\frac{1}{13}$
• C. $P ( A )=\frac{1}{13} ; P ( B )=\frac{1}{17}$
• D. $P(A)=\frac{16}{221} ; P(B)=\frac{4}{51}$

Answer 1

Answer: (B)

$ P ( A )= P \{( B \cap A ) \cup(\overline{ B } \cap A )\}= P ( B \cap A )+ P (\overline{ B } \cap A ) $
$= P ( B ) P ( A / B )+ P (\overline{ B }) P ( A / \overline{ B })=\frac{4}{52} \cdot \frac{3}{51}+\frac{48}{52} \cdot \frac{4}{51}=\frac{1}{13}$
$\text { also, } P ( B )=\frac{1}{13} $