Answer to Question #4372 in Statistics and Probability for David Atkins

Question

I flip a coin 50 times.
What is the probability I get at least one run of at least 4 'heads'.
Please show me the math.

Answer 1

I flip acoin 50 times. What is the probability of at least one run of at least 4
'heads'?
Let A-meansthe run of 4 “heads”. The probability of heads and tales is the same and equals
½ .
ProbabilityisP(A)=(1/2)^50 * (47*48*49*50/24+46*47*48*49*50/120+45*46*47*48*49*50/720+...+49*50/2+50+1)