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 $ $P(A)= \frac{10}{20} = \frac{1}{2}$
$\therefore P(B|A)= \frac{9}{19}$
$\therefore P (A \cap B) = P(A).P(B|A) =\frac{1}{2} \times \frac{9}{19}$
$= \frac{9}{38}$