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 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; 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

Answer 1

Answer:

Step-by-step explanation

:=log x + log y = log xy

for log xy to be positive, we have the following choices:

(1, 10), (10, 1), (10, 10), (5, 20), (20, 5), (2, 5), (5, 2)

So the probability = 7/400

Answer 2

Answer:

The probability that log x + log y is a positive integer is 7/400

Step-by-step explanation:

Step 1:

Given Data: log(x + y) = log x y

(Only positive integer possible are 1 and 2)

Step 2:

When x y = 10   & x y = 100

xy = 10   ( 1 x 10  , 2 x 5, 5 x 2, 10 x 1)

Step 3:

xy = 100  (5 x 20  , 10 x 10 , 20 x 5)

Total 7 cases out of 20 x 20 = 400

Step 4:

Probability is 7/400