From Stack Exchange:

• 50% of all people who receive a first interview receive a second interview
• 95% of your friends that got a second interview felt they had a good first interview
• 75% of your friends that DID NOT get a second interview felt they had a good first interview
If you feel that you had a good first interview, what is the probability you will receive a second interview?

The easiest way (at least for me) to go is to turn those percentages into some real numbers. For instance:
– 100 friends that got a second interview; 95 of them felt that they had a good first interview
– 100 friends that did NOT get a second interview; 75 of them felt that they had a good first interview.
Now, if you ignore the fact that it’s pretty difficult to have 200 friends (let alone the fact that they all applied for a job at Amazon 🙂 ), the numbers say that:
– 95 + 75 = 170 friends had a good feeling after the first interview
– but only 95 of them had a second interview
– so the probability of you having a second interview is 95 / 170 = 0.558.
In other words, if you felt good after the first interview, you have more than 50% chances that you get a second interview.

Image: HollywoodReporter.com

Now, if you come up with the answer 55.8% to your Amazon interviewer, I think you would get some points. But not all of them. Because in the logic below there are 2 hidden assumptions:
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As promised in the previous episode 🙂

Probability to have a duplicate (Y axis) by the number of stickers (X axis) – with an album size of 192 stickers:

The number of distinct stickers (Y axis) by the number of stickers (X axis) – with the album size of 192 stickers:

Made with JPGraph in a few minutes.

The previous post about Panini stickers got into some mathematical formulas. However, the 2 main conclusions were referring to the duplicates probability and distinct probability. That was the mathematical approach to the problem.
Below – the geeky one 🙂

1. Duplicates probability

In a Panini pack of 17 stickers (out of 192 possible stickers), there are 50% chances to have a duplicate.

The geeky way:
– generate a random array of ‘n’ integers in the range [1,192]
– calculate how many duplicates has the array
– repeat this a number of times to get a reliable view.

Results (PHP code at the end of the post):

Number of stickers - Probability of duplicate
10 - 20.47% 
11 - 25.8% 
12 - 31.2% 
13 - 37.13% 
14 - 40.6% 
15 - 45.47% 
16 - 47% 
17 - 53.4%
18 - 58.4% 
19 - 63.27% 
20 - 66.53% 
21 - 69.87% 
22 - 74.53% 
23 - 76.53% 
24 - 80.27% 
25 - 82.33% 
26 - 85.47% 
27 - 86.27% 
28 - 87.87% 
29 - 89.93% 
30 - 91.67% 
31 - 93.73% 
32 - 94.4% 
33 - 94.87% 
34 - 96.07% 
35 - 96.53% 
36 - 97.13% 
37 - 97.47% 
38 - 97.6% 
39 - 98% 
40 - 98.33% 

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