SOLUTION: if two cards are removed from a ordinary deck of card without replacement, what is the probability of drawing (a) a king followed by a heart (b) a face card followed by a "Three"

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Question 712590: if two cards are removed from a ordinary deck of card without replacement, what is the probability of drawing
(a) a king followed by a heart
(b) a face card followed by a "Three"
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
if two cards are removed from a ordinary deck of card without replacement, what is the probability of drawing
(a) a king followed by a heart
We must consider two case, the King CAN be a heart:

Case 1.  We draw the King of hearts and then we draw another heart

P(Case 1) = expr%281%2F52%29%2Aexpr%2812%2F51%29 = 12%2F%2852%2A51%29 

Case 2.  We draw the King of diamonds, spades or clubs and then we draw a heart

P(Case 2) = expr%283%2F52%29%2Aexpr%2813%2F51%29 = 39%2F%2852%2A51%29 


P(Case 1 OR Case 2) = P(Case 1) + P(Case 2) = 12%2F%2852%2A51%29 + 39%2F%2852%2A51%29 = %2812%2B39%29%2F%2852%2A51%29 = 51%2F%2852%2A51%29 = cross%2851%29%5E1%2F%2852%2Across%2851%29%29 = 1%2F52 

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(b) a face card followed by a "Three"
We only need to consider one case here, because the face card CANNOT be a "three":

[There are 12 face cards, the Jack, Queen, or King of 4 suits]

Probability = expr%2812%2F52%29%2Aexpr%284%2F51%29 = %2812%2A4%29%2F%2852%2A51%29 = 4%2F221

Edwin