Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How would I go about solving this problem?

What are the chances of at least $4$ heads if you flip a coin $5$ times

I constructed a tree diagram but I don't think that is correct. The answer I got was $\frac{1}{8}$.

share|cite|improve this question
up vote 2 down vote accepted

Each of the $2^5=32$ possible sequences of heads and tails is equally likely. There's one sequence with all heads, and there are $5$ different sequences with four heads, corresponding to the $5$ possible positions of the one tails result. Thus the probability is $(1+5)/32=6/32=3/16$.

share|cite|improve this answer

Apply Bernoulli's Formula:


share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.