One letter is picked at random from each of the words LUNAR and LANDER. The chance that the letters picked from both words belong to the word PRAGYAN is

Correct option is A

Given:
Words: LUNAR and LANDER
We need to find the probability that the letters picked from both words belong to the word PRAGYAN.

Solution:
Letters in the word PRAGYAN:
The word PRAGYAN has the following unique letters:
P, R, A, G, Y, N.

Letters in LUNAR:
The letters in LUNAR are:
L, U, N, A, R
We need to find how many of these belong to PRAGYAN:
Common letters = N, A, R
So, the probability of picking a letter from LUNAR that belongs to PRAGYAN is: 

​$$P(\text{LUNAR}) = \dfrac{3}{5}$$​​

(since there are 3 valid letters out of 5).

Letters in LANDER:
The letters in LANDER are:
L, A, N, D, E, R
Common letters with PRAGYAN = N, A, R
So, the probability of picking a letter from LANDER that belongs to PRAGYAN is:

$$P(\text{LANDER}) = \dfrac{3}{6} = \dfrac{1}{2}$$​​
(since there are 3 valid letters out of 6).
​
Total Probability:
The total probability of picking one letter from each word such that both belong to PRAGYAN is the product of the individual probabilities:
​$$\text{Total probability:} \\P(\text{both letters in PRAGYAN}) = \dfrac{3}{5} \times \dfrac{1}{2} = \dfrac{3}{10}$$​​

Final Answer: (A) 3/10