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14 | 14 | The way the question is worded expresses this scenario as something less intuitive and you'll need to reason it out before answering. |
15 | 15 |
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16 | 16 |
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17 | | -Questions about card drawing should be done using the combination formula. |
18 | | -It is a useful technique , since you can answer very complicated card-related questions with it. |
| 17 | +Questions about card drawing should be answered using the combination formula. |
| 18 | +It is a useful technique since you can answer very complicated card-related questions with it. |
19 | 19 | For instance, if I draw 6 cards, what is the probability of drawing exactly two aces and one king? |
20 | 20 | The answer is |
21 | 21 | \begin{align} |
|
42 | 42 | &= \frac{ 4 \times 3 }{ 52 \times 51 } \nonumber |
43 | 43 | \text{.} |
44 | 44 | \end{align} |
45 | | -But this is not the answer the interviewer wants. |
46 | | -They want you to use the following, simpler method: |
| 45 | +For this question, there is another method: |
47 | 46 | \begin{align*} |
48 | 47 | P(\text{Drawing two aces}) |
49 | 48 | &= |
|
56 | 55 | \times |
57 | 56 | \frac{3}{51} |
58 | 57 | \end{align*} |
59 | | -and then they want you to simplify the fraction in your head, \emph{quickly}: |
| 58 | +and then you need to simplify the fraction in your head, \emph{quickly}: |
60 | 59 | \begin{align*} |
61 | 60 | \frac{4}{52} |
62 | 61 | \times |
|
71 | 70 | \end{align*} |
72 | 71 | During my interview, I first tried to use the method in |
73 | 72 | \eqref{eq:drop20cards:cardmath}, |
74 | | -but from the incredulity in my interviewer's voice he probably was not familiar with the technique. |
| 73 | +but from the incredulity and confusion in my interviewer's voice he probably was not familiar with the technique. |
75 | 74 | Many interviewers who ask statistics and probability only took one brief statistics course and---outside of some brainteasers they looked up---aren't aware of all the techniques and nuances, nor the differences in jargon.\footnote{This has been exacerbated by the redefinition of many statistical concepts within Machine Learning.} |
76 | | -Fortunately I knew how to use the simpler method, but under pressure I was unable to perform the mental arithmetic fast enough. |
| 75 | +Fortunately I knew about both methods, but under pressure I was unable to perform the mental arithmetic fast enough. |
77 | 76 | \end{answer} |
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