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Ask The Wizard #384

If:

  • a2 – bc = 5
  • b2 – ac = 7
  • c2 – ab = 9

Then what are a, b, and c?

anonymous

Solution 1:

  • a = -sqrt(1805/315) =~ -2.393775
  • b = +(2/19)×sqrt(1805/315) =~ 0.251976
  • c = +(23/19)×sqrt(1805/315) =~ 2.897728

Solution 2:

  • a = +sqrt(1805/315) =~ +2.393775
  • b = -(2/19)×sqrt(1805/315) =~ -0.251976
  • c = -(23/19)×sqrt(1805/315) =~ -2.897728

Here is my solution (PDF).

What is the expected number of spins in roulette to see five reds or five blacks in a row?

anonymous

The answer is 3872789/118098 =~ 32.79301089 spins.

 

Here is my solution (PDF).

Upon opening a Facebook account, the following are the average number of ads for fake stamps received by number of days since opening the account:

  • 4 ads within one day.
  • 16 ads within two days.
  • 36 ads within three days.

What is the expected number of hours until the first ad for fake stamps appears?

anonymous

The answer is sqrt(π)/4 days =~ 10 hours, 38 minutes, 5 seconds.

 

Here is my solution (PDF).

This question is asked and discussed in my forum at Wizard of Vegas.