Question

A bag contains $20$ tickets, numbered $1$ to $20$. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.

• A. $\frac{9}{38}$
• B. $\frac{16}{35}$
• C. $\frac{7}{38}$
• D. $\frac{17}{30}$

Answer 1

Answer: (A)

Let $A$ be the event of drawing an even numbered ticket in first draw and $B$ be the event of drawing an even numbered ticket in second draw.
$\therefore$ Required probability $=P(A\cap B)=P(A).P(B|A)$
$A=\{2,4,6,8,10,12,14,16,18,20\}$
$\therefore$ $P(A)=\frac{10}{20}=\frac{1}{2}$
$\therefore P(B|A)=\frac{9}{19}$
$\therefore P(A\cap B)=P(A).P(B|A)=\frac{1}{2}\times \frac{9}{19}$
$=\frac{9}{38}$