Fair Coin: Flip 4 times
获得1个Head的概率
P(exactly 1 “heads”) = P(HTTT) +P(THTT)+P(TTHT)+P(TTTH)= $\frac{1}{16}$+$\frac{1}{16}$+$\frac{1}{16}$+$\frac{1}{16}$=1/4
获得2个Head的概率
4次里面选2次 $C_4^2=\frac{43}{21} = 6$
P(exactly 2 “heads”) =$\frac{C_4^2}{16}$ = 3/8
Fair Coin: Flip 5 flips
获得3个Head的概率
5次里面选3次 $C_5^3=\frac{543}{321} = 10$
P(exactly 3 “heads”) =$\frac{C_5^3}{32} $ = 5/16
Fair Coin: Flip n flips
获得k个Head的概率
n次里面选k次 $C_n^k= \frac{\frac{n!}{(n-k!)}}{k!}=\frac{n(n-1)…(n-k+1)}{k(k-1)…1}$
all the probability = $2^{n}$
P(exactly k “heads”) =$\frac{n(n-1)…(n-k+1)}{2^{n}k*(k-1)…1}$
