basic probability question cards

you’ve drawn your two cards and, tragically, neither of them is an ace.

Your friend is feeling generous: she lets you draw ten additional cards. Still no luck. You know there are 40 cards remaining in the deck, of which four are aces.

If your friend now draws two cards, what’s the probability she gets exactly one ace?

I thought the prob are independent: so the prob to get an ace on the first card is 4/40, and the second 36/40 (not being an ace), I multiplied them and give me some prob. but I am not sure if the logic I am using is right. Someone does it know if this is the correct logic?
thanks

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Well, either the first is an ace, or the second, but not both. The other card can be any one of 36. Can you find at least the number of ways of drawing favourably now?
– ذ°رپر‚ذ¾ذ½ ذ²ر–ذ»ذ»ذ° ذ¾ذ»ذ¾ر„ ذ¼رچذ»ذ»ذ±رچر€ذ³
2 days ago

  

 

well yes, I thought the prob are independent: so the prob to get an ace on the first card is 4/40, and the second 36/40 (not being an ace), I multiplied them and give me some prob. but I am not sure if the logic I am using is right. this is not a homework. Sorry my first time useing this, I forgot to include my thinking..
– Eliec
2 days ago

  

 

Why is not drawing an ace “tragic”?
– Henning Makholm
2 days ago

  

 

Add that comment into your question please.
– barak manos
2 days ago

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2 Answers
2

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Suppose the probability that she gets exactly one ace is P.

Then P= probability (that first card is an ace and second one is not) +
probability (that first card is not an ace but second is an ace)
=4403639+3640439\frac{4}{40}\frac{36}{39}+\frac{36}{40}\frac{4}{39}
=12/6512/65

That’s the answer.

(41)⋅(40−42−1)(402)\frac{\binom{4}{1}\cdot\binom{40-4}{2-1}}{\binom{40}{2}}

  

 

ok thanks, but what is wrong with 4/40*36/40, to find only 1 ace?
– Eliec
2 days ago

  

 

Thank you Isha Dhiman!!
– Eliec
2 days ago

  

 

@Eliec: The numerator is correct, the denominator is not. Once you choose the first card out of the 4040 cards, you have only 3939 cards remaining to choose the second card from.
– barak manos
2 days ago

  

 

got it now from the Isha! thank you Barak!
– Eliec
2 days ago