Question

If a biased coin with probability of heads 2/3is tossed 3 times, what is the probability of getting all heads

Answer 1

Answer:

$\frac{8}{27}$

Step-by-step explanation:

1) We have, biased coin with probability of getting head ,p = 2/3.

Let X  be a random variable of getting heads.

Then,

We know,

Probability of getting 'x' heads out of 3,

$P(X=x)^3C_x(\frac{2}{3})^x(\frac{1}{3})^{3-x}$

2) Now, We need probability of getting  all heads.

   That is,

$P(X=3)=\:^3C_3\:(\frac{2}{3})^3(\frac{1}{3})^{3-3}\\ \\=1*\frac{8}{27}*(\frac{1}{3})^0=\frac{8}{27}$