Question

Two decks of cards are there. Each deck contains 20 cards, with numbers from 1 to 20 written on them. A card is drawn of random from each deck, getting the numbers x & y. What is the probability that log x +log y is a positive integer. Logs are taken to the base 10 3/200 (b) 29/200 (c) 7/400 (d) 1/50

Answer 1

[Nice Question]

$\textbf{My solution}$ :----

log x+log y = log(xy)

log (base 10)(xy) is integer when xy is 10^n

[ n=1,2,3....]

(1) 10¹ = 10,

5*2 --- 2 combinations

or

10*1 ----2 combinations

( Total = 4 combinations )

(2) 10² = 100,

5*20 --- 2 combinations

or

10*10----1 combination

(Total = 3 combinations)

Overall = 7 combinations are integers

total no of combinations possible = 20*20 = 400

Probabilility = 7/400 (Ans.)

$\color{red}{Mark\: as\: Brainlist}$