Question

A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

• A. $\frac{3}{16}$
• B. $\frac{5}{32}$
• C. $\frac{5}{16}$
• D. $\frac{5}{8}$

Answer 1

The correct option is B $\frac{5}{32}$

Let H denote the head,
T the tail.
* Any of the head or tail
$P\left(H\right)=\frac{1}{2},P\left(T\right)=\frac{1}{2}P(\ast )=1$
$HHHH\ast \ast \ast ={\left(\frac{1}{2}\right)}^4\times 1=\frac{1}{16}THHHH\ast \ast ={\left(\frac{1}{2}\right)}^5\times 1=\frac{1}{32}\ast THHHH\ast ={\left(\frac{1}{2}\right)}^5\times 1=\frac{1}{32}\ast \ast THHHH={\left(\frac{1}{2}\right)}^5\times 1=\frac{1}{32}\frac{5}{32}$