Question

Choose the correct option from the given alternatives:

If X ~ B(4, p) and P(X = 0) = `16/81`, the P(X = 4) = ______

Options

• `1/16`

• \[\frac{1}{81}\]

• \[\frac{1}{27}\]

• \[\frac{1}{8}\]

Answer 1

\[\frac{1}{81}\]

Hint:

P(X = 0) = `"^4C_0  p^0  q^4 = 16/81`

∴ `"q"^4 = (2/3)^4`

∴ q = `2/3`

∴ p = 1 - q = `1 - 2/3 = 1/3`

∴ P(X = 4) = `"^4C_4 p^4 q^0 = (1/3)^4 = 1/81`