Solutions to Practice Problems for  the Lander Math Contest
Module 7, Solutions (19-21)

19) The probability of not getting 3 once is 5/6, then not
getting 3 five times in a row is (5/6)^5 ≈ 0.4019 .

20) Let us first calculate the probability of 7 successful throws
out of 7: 0.65^7 . The event “at most 6 successful throws out
of 7” actually means “not 7 out of 7”: 1-0.65^7 ≈ 0.9510

21) We pick up a normal coin with the probability 5/12 and
get 3 heads and one tail with the probability 1/2^4. If we pick
two-sided heads or two-sided tails coin, we’ll never get 3
heads and one tail when tossing this coin four times. That is
why the probability that a coin taken at random from the bag
and turns out to be exactly 3 heads and one tail is 5/12×1/2^4
≈ 0.026