Alex : Hey Bob, I think this coin is biased; I flipped it a few times and it always lends Tail. I think p, the probability of landing Head, must be less than 5%. Can you take a look? Bob: Seriously? I bet it's fair, that is I think p = 1/2. Let me flip it three times and count the number of Heads. If the number of Heads is smaller than some threshold t, then I will buy you dinner. Otherwise, you will buy me dinner.
Alex: Wow Bob, okay! I will go ahead and reserve a fancy restaurant.
Bob: One last thing, though, just to make things fair: pick any t you want, but let's keep the proba- bility that I buy you dinner even if I'm right (that is, even if the truth is p= 1/2) below 10% please.
Alex: Go away, Bob! Stop wasting my time!
Question: why did Alex get mad?

See below

Step-by-step explanation:

Alex finally understands how Bob was trying to trick him into winning the bet because of how he puts in the condition for probability being less than 10%. Whichever way the outcome of the coin toss turns out to be, it will be in Bob's favor and Alex will lose the bet. If the coin is flipped 3 times, the probability of having heads exactly twice is

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

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