Home> Questions>Q 5330
Next
In Process

AcedStudy Latest Questions

ernstmndza
  • 0
Tyro
Asked: 2021-03-31T14:18:47+00:00 In:

Statistics and Probability: Probability Distribution

  • 0

A family has three children. Let X represent the number of boys. Construct a probability distribution

probabilityquestion

You must login to add an answer.

Need An Account,

1 Answer

  2. acedstud

    Given a family of 3 children, thus n=3. We assume that there is an equal chance of giving birth to a boy as there is for a girl. Thus, the probability of success (a child being a boy) is 0.5.

    The scenario describes a binomial distribution and the probability that a random variable, X, following a binomial distribution is equal to the value, x, is given by P(X=x)= ^nC_xp^x(1-p)^{n-x}, where p is the probability of success.

    To construct the probability distribution, we find the probability that X is from 0 to n=3.

    P(X=0)=^3C_0(0.5)^0(1-0.5)^{3-0}=^3C_0(0.5)^0(0.5)^{3}=1\times1\times0.125=0.125.

    P(X=1)=^3C_1(0.5)^1(1-0.5)^{3-1}=^3C_1(0.5)^1(0.5)^{2}=3\times0.5\times0.25=0.375.

    P(X=2)=^3C_2(0.5)^2(1-0.5)^{3-2}=^3C_2(0.5)^2(0.5)^{1}=3\times0.25\times0.5=0.375.

    P(X=3)=^3C_3(0.5)^3(1-0.5)^{3-3}=^3C_3(0.5)^3(0.5)^{0}=1\times0.125\times1=0.125.

    Therefore, the probability distribution is

    x 0 1 2 3
    P(x) 0.125 0.375 0.375 0.125

Related Questions