Can you explain this probability answer?

[RedString]

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express answer as simplified fraction.

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We came to the answer 25/52.

Apparently it was 25/102.

--

Our thinking:

26 out of 52 playing cards would be black. The second card taken would be 25 out of 51. How did the answer get 102? I figured it would be 26/52 multiplied by 25/51.


Sorry for bringing homework here, it's just that the statistics teacher my girlfriend has supposedly doesn't teach whatsoever in class and I have no experience at all in statistics. Looking this stuff up online can be difficult, usually just takes you to more abstract equations that I don't understand.

 

[gophins72]

1/2 * 25/51 = 25/102


26/52 = 1/2

 

[the DRIZZLE]

you are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express answer as simplified fraction.

--

we came to the answer 25/52.

Apparently it was 25/102.

--

our thinking:

26 out of 52 playing cards would be black. The second card taken would be 25 out of 51. How did the answer get 102? I figured it would be 26/52 multiplied by 25/51.


Sorry for bringing homework here, it's just that the statistics teacher my girlfriend has supposedly doesn't teach whatsoever in class and i have no experience at all in statistics. Looking this stuff up online can be difficult, usually just takes you to more abstract equations that i don't understand.

26/52 * 25/52= 1/2 * 25/52= 25/104

 

[Pardus]

1 for good
2 for bad

 

[gophins72]

also, i think your answer would probably be right if you reduce the fraction down to its lowest numerator/denominator:

26/52 * 25/51 = 650/2652 = (divide top and bottom by 26) = 25/102

 

[RedString]

also, i think your answer would probably be right if you reduce the fraction down to its lowest numerator/denominator:

26/52 * 25/51 = 650/2652 = (divide top and bottom by 26) = 25/102

That helped her understand it better.

I like the first way, I was just having problems earlier since I wasn't thinking of it as fractions and that /51 halved would have made it /102.


Preciate the help guys. She has been slacking off lately and didn't catch up during spring break so we've got like 4-5 more sections to do. Fun fun.

 

[Mo0o]

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express answer as simplified fraction.

--

We came to the answer 25/52.

Apparently it was 25/102.

--

Our thinking:

26 out of 52 playing cards would be black. The second card taken would be 25 out of 51. How did the answer get 102? I figured it would be 26/52 multiplied by 25/51.


Sorry for bringing homework here, it's just that the statistics teacher my girlfriend has supposedly doesn't teach whatsoever in class and I have no experience at all in statistics. Looking this stuff up online can be difficult, usually just takes you to more abstract equations that I don't understand.

Seems like you have it right but dont know how to multiply fractions? (26/52) * (25/51) = 25/102

 

[Schfifty Five]

26/52 * 25/52= 1/2 * 25/52= 25/104

The bolded part is wrong since the OP mentioned "without replacement" so it should be 25/51.