# Thread: Counting Principles, card 1..50 and one number is twice the other

1. ## Counting Principles, card 1..50 and one number is twice the other

There are 50 cards numbered from 1 to 50.
Two different cards are chosen at random. What is the probability that one number is twice the other number?

The answer is 2*25 / 50*49

I tried to split it in two cases. Case1, I get the lower card first (2,4) and case2, I get the higher number first (4,2).

case1:

__ __ First place has 25 choices (1-25), second place then has only 1 choice

case2:

__ __ First place has 25 choices (26-50), second place then has only 1 choice

Then I would add it up: 1*25 + 1*25

The total amount of ways to combine two cards would be 50*49 (First place has 50 choices and second place has 50-1 card which was already used)

The probability is then 1*25 + 1*25 / 50*49

Is this approach correct. The answer indicates that I have to multipy (2*25).

Thanks.

2. The answer is 2*25 / 50*49
It seems that you came up with the same answer: (1*25 + 1*25) / 50*49.

Is this approach correct. The answer indicates that I have to multipy (2*25).
I am not sure I understood what you said. Multiply by (2*25)?

,

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### there are 50 cards numbered from 1to 50 two different cards are chosen at random what is the probability thatone number is twice the other number o

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