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# Probability: Intersection of Dependent Events

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63
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Hi, so this is a question that I got wrong on my HW and I don't know why or what the correct answer is.

 Two cards are drawn at random from a deck of 52 cards without replacing the first card before choosing the second card. What is the probability that the first card is a heart and the second card is a number card that is black?   Enter your final answes as reduced fractions.

My answer was $$\frac{5}{51}$$

My formula set up:

$$\frac{13}{52}\times\frac{20}{51}=0.980392157=\frac{5}{51}$$

Apr 10, 2021

#1
+31586
+3

13 / 52 is correct..... then there are 51 cards left of which  18 are black number cards    ace is not a number   ( not 20)

Apr 10, 2021
edited by Guest  Apr 10, 2021
edited by ElectricPavlov  Apr 10, 2021
#2
+118626
+2

P(first card  is a heart  and second  is  a black "number" card)  =

1/4   *   18 / 51   =

1/4  *  6 / 17  =

6  / 68   =

3 / 34

Apr 10, 2021