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I throw a coin $n$ number of times.

1) What's the probability of the number of times of coming up tails is divisible by $4$?

2) What's the probability that it's not divided by number $4$?

My reasoning is to tackle by going one by one.

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1 Answer 1

$$\left(\frac12\right)^n \sum \binom n k [0\le k\le n][k\equiv 0\pmod 4]$$

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