Question

Let X be a binomial random variable with p = 0.7

1. a) For n = 3, find P(X=1)

2. b) For n = 5, find P(X≤3)

Answer 1

Solution

Given that ,

p = 0.7

1 - p = 1 - 0.7 = 0.3

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

(a)

n = 3

x = 1

P(X = 1) = ((3! / 1! (2)!) * 0.7¹ * (0.3)²

= 0.189

Probability = 0.189

b)

n = 5

P(x 3) = P(X = 0) + P(x = 1) + P(x = 2) + P(x = 3)

= ((5! / 0! (5)!) * 0.7⁰ * (0.3)⁵ +  ((5! / 1! (4)!) * 0.7¹ * (0.3)⁴ +  ((5! / 2! (3)!) * 0.7² * (0.3)³ +  ((5! / 3! (2)!) * 0.7³ * (0.3)²

= 0.4718

P(x 3) = 0.4718