Business Majors Suppose 30 of business majors major in accou

Business Majors

Suppose 30% of business majors major in accounting. You take a random sample of 3 business majors.

Please show how the answer is worked.

        1.   {Business Majors Narrative} What is the chance that they all major in accounting?

        2.   {Business Majors Narrative} What is the chance that at least one majors in accounting?

        3.   {Business Majors Narrative} What is the chance that exactly one majors in accounting?

        4.   {Business Majors Narrative} What is the chance that none of them major in accounting?

I have the formulas, but I can not get to the answer.

Solution

Probability that a buisness major majors in accounting is 0.3 i.e 30%

Hence probability that a buisness major will not major in accounting is 1- 0.3 = 0.7

3 buisness majors are taken i.e n = 3.

X be the random variable: the number of persons among these three majoring

So it could be 0 of them majoring , 1, 2 or 3 of them majoring. So here X is a binomial random variable and hence we can use the formula we have to find the probability

P(X= x)= ⁿC_x p^xq^n-x

1. chance that they all major in accounting = ³C₃(0.3)³(0.7)^3-3 = .3³ = 0.027

2. Chance that atleast one of them majors means it could be one, or two or three of them

so its P(X=1)+P(X=2)+P(X=3) = ³C₁(0.3)¹(0.7)^3-1+³C₂(0.3)²(0.7)^3-2+³C₃(0.3)³(0.7)^3-3  =0.441+0.378+0.027 = 0.846

3. P(X=1)= ³C₁(0.3)¹(0.7)^3-1=0.441

4 P(X=0) = ³C₀(0.3)⁰(0.7)^3-0 =0.343