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 and y What is the probability that log x + log y is a positive integer. Logs are taken to the base 10.
options:
a. 3/200
b. 29/200
c. 7/400
d. 1/50

• log x+log y=log(xy)
  log (base 10)(xy) is integer when xy is 10^n,where n=1,2,3....so on
  1. 10^1=10, 5*2--- 2 combinations or 10*1----2 combinations-------total 4 combinations
  2. 10^2=100, 5*20---2 combinations or 10*10----1 combination-----total 3 combinations
  all total 7 combinations are integers
  total no of combinations possible=20*20
  probabilility=7/(20*20)=7/400
  
• 8 years agoHelpfull: Yes(31) No(6)
• Log x + log y = log(xy)
  log xy is integer when (x,y) = (1, 10), (10, 1), (10, 10), (5, 20), (20, 5), (2, 5), (5, 2)
  So required probability = 7/400
• 8 years agoHelpfull: Yes(16) No(7)
• log x+log y=log(xy)
  log (base 10)(xy) is integer when xy is 10^n,where n=1,2,3....so on
  1- (10,1),(10,2),(10,3)...(10,9),(10,11).... upto 20. so total 19 combinations
  2- (20,1),(20,2),(20,3)...(20,19), so total 19 combinations
  3-(5,even numbers upto 20)=10 combinations
  4-(15,even numbers upto 20_=10 combinaions
  so total 58 combination.
  so 58/400=29/200
  m/
• 8 years agoHelpfull: Yes(0) No(17)