Question

In each part, assume the random variable ? has a binomial distribution with the given parameters. Compute the probability of the event.

(a) ?=3,?=0.1
??(?=3)=

(b) ?=3,?=0.8
??(?=1)=

(c) ?=6,?=0.1
??(?=1)=

(d)  ?=5,?=0.5
??(?=4)=

Answer 1

Solution

Given that ,

p = 0.1

q = 1 - p = 1 - 0.1 = 0.9

n = 3

Using binomial probability formula ,

P(X = x) = (_n C _x) * p ^x * (1 - p)^{n - x}

P(X = 3) = (₃ C ₃) * 0.1 ³ * (0.9)⁰

^=0.0010

^{probability=0.0010}

^(b)

Solution

Given that ,

p = 0.8

q = 1 - p = 1 - 0.8 = 0.2

n = 3

Using binomial probability formula ,

P(X = x) = (_n C _x) * p ^x * (1 - p)^{n - x}

P(X = 1) = (₃ C ₁) * 0.8 ¹ * (0.2)²

^=0.0960

^{probability=0.0960}

^(c)

Solution

Given that ,

p = 0.1

q = 1 - p = 1 - 0.1 = 0.9

n = 6

Using binomial probability formula ,

P(X = x) = (_n C _x) * p ^x * (1 - p)^{n - x}

P(X = 1) = (₆ C ₃) * 0.1 ¹ * (0.9)⁵

^=0.3543

^{probability=0.3543}

^(d)

Solution

Given that ,

p = 0.5

q = 1 - p = 1 - 0.5 = 0.5

n = 5

Using binomial probability formula ,

P(X = x) = (_n C _x) * p ^x * (1 - p)^{n - x}

P(X = 4) = (₅ C ₄) * 0.5 ⁴ * (0.5)¹

^=0.1563

^{probability=0.1563}