Question 1210425
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Answers:
(a)  <font color=red>1/17</font>
(b)  <font color=red>4/17</font>
(c)  <font color=red>13/51</font>
(d)  <font color=red>4/51</font>



Explanations


Part (a)


There are 4 copies of cards with the label "3" (one for each suit).
Since Sara is not replacing the 3 of hearts she selects, there are 4-1 = 3 copies remaining. This is out of 52-1 = 51 cards.


3/51 = (1*3)/(17*3) = <font color=red>1/17</font> is the probability of another 3 being selected if the first card is not replaced.


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Part (b)


There are 52 cards in a deck. 
52/4 = 13 of which are hearts
(ace, 2 through 10, jack, queen, king)
This excludes jokers.


If 3 of hearts is the first card, and not put back or replaced, then there would be 13-1 = 12 hearts remaining out of 52-1 = 51 cards
12/51 = (4*3)/(17*3) = <font color=red>4/17</font> is the answer to part (b)


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Part (c)


There are 13 clubs out of 52-1 = 51 cards remaining.
This leads directly to <font color=red>13/51</font> which cannot be reduced further.
Note I did not subtract 1 from the clubs since the sets "hearts" and "clubs" are mutually exclusive. There's no overlap.


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Part (d)


There are 4 copies of 7 out of 52-1 = 51 cards remaining.
Therefore the answer is <font color=red>4/51</font>
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