Draw1King - Recall the practice test problem concerning...

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Recall the practice test problem concerning drawing exactly 1 King from a standard deck of 52 playing cards. The argument was made in class that one can compute the answer beginning with the probability of drawing one King being 4 52 and multiplying by other similar fractions to obtain the answer. To understand this better we consider a smaller case problem. Suppose we have a deck of 5 playing cards that we shall label The first two are Kings and the last three are distinct cards but Not Kings. We are asked to obtain the probability of drawing exactly 1 King in a hand of 3 cards. 1 2 1 2 3 , , , , K K N N N . The sample space can easily be enumerated in this case: 1 2 1 1 2 3 1 2 2 2 1 2 1 2 3 2 1 3 1 1 2 2 2 3 1 1 3 1 2 3 K K N K N N K K N K N N K K N K N N K N N K N N K N N N N N Clearly [ ] 6 Exactly 1 King (just count the sample points). 10 P = According to the formula we learned in class the answer is [ ] 2 3 1 2 2 3 6 Exactly 1 King . 5 10 10 3 P ⎞⎛ ⎟⎜ × ⎠⎝ = = = If we try the approach suggested by students in class, however, we have
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