Problema Solution
A weighted coin lands on heads 80% of the time, the coin is flipped twenty times what is the probability of observing fewer than nineteen heads?
Answer provided by our tutors
the event is flipping a coin
the probability of getting a head is p = 0.80
the coin is flipped 20 times means we have 20 independent events
the probability of getting heads on all 20 flips is p^20 = 0.80^20
the probability of getting heads on 19 flips is p^20 = 0.80^19
the probability of getting fewer then 19 heads = 1 - (the probability of getting 20 heads + the probability of getting 19 heads) that is
1 - (p^20 + p^19) = 1 - (0.80^20 + 0.80^19) = 0.9741 or 97.41%