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)

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