Question

A bag contains $19$ tickets numbered from $1$ to $19$. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number is

• A. $\frac{9}{19}$
• B. $\frac{8}{18}$
• C. $\frac{9}{18}$
• D. $\frac{4}{19}$

Answer 1

The correct option is D

$\frac{4}{19}$

Explanation for correct answer:

Step-1: Finding probability that the ticket taken from bag first times.

From the question, we have total number of tickets in bag from $1\mathrm{to}19=1,2,3,......19$ is $19$

Total even number of tickets in a bag $2,4,6,......18$ is $9$.

Probability that a ticket drawn from bag $A$is $\frac{9}{19}$

Step-2: Finding probability that the ticket taken from the bag second times without replacement.

After completing first experiment,

Total number of ticket in a bag are $\left(19-1\right)=18$

Total even number of ticket are $\left(9-1\right)=8$

Probability that a ticket drawn from the bag $A$ is $\frac{8}{18}$

The probability that both the tickets will show even number is $\frac{9}{19}\times \frac{8}{18}=\frac{4}{19}$

Therefore, correct answer is option $\left(D\right)$