Answer:
Option A: ![$ \frac{\textbf{2}}{\textbf{9}} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B%5Ctextbf%7B2%7D%7D%7B%5Ctextbf%7B9%7D%7D%20%24)
Step-by-step explanation:
Given there are 10 cards viz: 1, 2, 3, 4, . . . , 10
We find the probability of drawing two cards less than six, without replacing the first card.
Draw 1:
There are 5 cards with value less than 6. 1, 2, 3, 4, 5
The total number of cards is 10.
The probability of the number being less than 6 = ![$ \frac{number \hspace{1mm} of \hspace{1mm} cards \hspace{1mm} less \hspace{1mm} than \hspace{1mm} 6}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7Bnumber%20%5Chspace%7B1mm%7D%20of%20%5Chspace%7B1mm%7D%20cards%20%5Chspace%7B1mm%7D%20less%20%5Chspace%7B1mm%7D%20than%20%5Chspace%7B1mm%7D%206%7D%7Btotal%20%5Chspace%7B1mm%7D%20number%20%5Chspace%7B1mm%7D%20of%20%5Chspace%7B1mm%7D%20cards%7D%20%24)
![$ = \frac{5}{10} $](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B5%7D%7B10%7D%20%24)
Draw 2:
We are again drawing a card without replacing the card that was drawn earlier. This makes the total number of cards 9.
Also, the number of cards less than 6 will now be: 4.
Therefore, probability of drawing a number less than 6 without replacing
![$ = \frac{4}{9} $](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B4%7D%7B9%7D%20%24)
Since, both draw 1 and draw 2 are happening we multiply the two probabilities. We get
![$ \textbf{P} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{5}}{\textbf{10}} \hspace{1mm} \times \hspace{1mm} \frac{\textbf{4}}{\textbf{9}} $](https://tex.z-dn.net/?f=%24%20%5Ctextbf%7BP%7D%20%5Chspace%7B1mm%7D%20%5Ctextbf%7B%3D%7D%20%5Chspace%7B1mm%7D%20%5Cfrac%7B%5Ctextbf%7B5%7D%7D%7B%5Ctextbf%7B10%7D%7D%20%5Chspace%7B1mm%7D%20%5Ctimes%20%5Chspace%7B1mm%7D%20%5Cfrac%7B%5Ctextbf%7B4%7D%7D%7B%5Ctextbf%7B9%7D%7D%20%24)
![$ \therefore P = \frac{\textbf{2}}{\textbf{9}} $](https://tex.z-dn.net/?f=%24%20%5Ctherefore%20P%20%3D%20%5Cfrac%7B%5Ctextbf%7B2%7D%7D%7B%5Ctextbf%7B9%7D%7D%20%24)
Hence, OPTION A is the required answer.