getting 3 five times in a row is (5/6)^5 ≈ 0.4019 .

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

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