Correct answer is A.
The probability distribution of X is:
![](https://www.sarthaks.com/?qa=blob&qa_blobid=6576049191328376440)
We Know that
![](https://www.sarthaks.com/?qa=blob&qa_blobid=6351442076078528706)
Therefore,
⇒ 2p + 2p + 3p + p2 + 2p2 + 7p2 + 2p = 1
⇒ 10p2 + 9p - 1 = 0
⇒ 10p2 + 10p - p -1 = 0
⇒ 10p(p + 1) -1(p + 1) = 0
⇒ (10p - 1)(p + 1)
10p - 1 = 0 or p + 1 = 0
p = \(\frac{1}{10}\) or p = -1
We considered p = \(\frac{1}{10}\) because p is a probability and probability cannot be in negative
Option (B) is incorrect because p is a probability and probability cannot be in negative
Option (C) is incorrect because p is a probability and probability cannot be in negative
Option (D) is incorrect because by putting p = \(\frac{1}{5},\) the sum total of pxi is not equal to 1