Question

100 point to the first correct answer

Answer 1

Answer:

X ~ B(n, p)

Given: X ~ B(2, 5/17)

⇒  n = 2

⇒  p = 5/17

Binomial distribution formula:

$\sf P(X = x) = nC_x (1-p)^{(n-x)}p^x$

As n = 2, calculate P(X = 0), P(X = 1) and P(X = 2):

$\sf P(X = 0) = 2C0 (\frac{12}{17})^{(2-0)}(\frac{5}{17})^0=\dfrac{144}{289}}$

$\sf P(X = 1) = 2C1 (\frac{12}{17})^{(2-1)}(\frac{5}{17})^1=\dfrac{120}{289}}$

$\sf P(X = 2) = 2C2 (\frac{12}{17})^{(2-2)}(\frac{5}{17})^2=\dfrac{25}{289}}$

**Probability Distribution Table attached**