Question

Let X ∼ B(n = 10, p = 0.2). Find:
(i) P (X = 1).
(ii) P (X ≥ 1).
(iii) P (X ≤ 8).

Answer 1

Please see the attachment

Answer 2

Answer:

2 * (0.8)⁹

1 -  (0.8)¹⁰

1  - 39 * (0.2)¹⁰

Step-by-step explanation:

n = 10

p = 0.2

q = 1 - 0.2 = 0.8

P (X = 1) = ¹⁰C₁ p¹ q⁹

= 10 * (0.2) * (0.8)⁹

= 2 * (0.8)⁹

P (X ≥ 1)  = 1 - P(0)   =  1  -  ¹⁰C₀ p⁰ q¹⁰

= 1 -  (0.8)¹⁰

P (X ≤ 8) = 1 - P(9) - P(10)

= 1  - ¹⁰C₉ p⁹ q¹ - ¹⁰C₁₀ p¹⁰ q⁰

= 1 - 10 (0.2)⁹(0.8) - (0.2)¹⁰

= 1  - (0.2)⁹ ( 8 - 0.2)

= 1  - (0.2)⁹ ( 7.8)

= 1  - 39 * (0.2)¹⁰