Each time an experiment is conducted, the probability of success is 0.4. When this experiment is repeated, the results of each repetition of the experiment are independent of one another. Let the positive integer n be the number of times the experiment must be repeated until it succeeds for the first time. The integers x and y are positive. The ratio of the probability that n = x to the probability that n = y is 27/125.

Select two numbers that are consistent with the information that is given. In the first column, select the row that shows the value of x, and in the second column, select the row that shows the value of y. Make exactly one selection for each column.

X, Y=
a.3
b.7
c.8
d.10
e. 12

OA is X=D, Y= B

Just wanted to make sure if my method was correct-

Since we are asked that the experiment was conducted until we succeeded, we can deduce that fpr as long as we conducted the experiment, the result was a failure. P(failure)= 1- P(success)= 1-0.4= 0.6

P(n=x)= 0.6*0.6*0.6*....x times= 0.6^x.
Similarly (n=y)= 0.6^y

Ratio is given-

0.6^x/0.6^y= 27/125
0.6^(x-y)= (3/5)^3

Equating the powers, we get x-y= 3 (since 3/5=0.60)

Therefore among the given options, [spoiler]X= 10 [/spoiler]and [spoiler]Y= 7[/spoiler]