Probability for college

Question

Question

The probability that a student entering college will graduate is 0.4. Determine the probability that out of 10 students:

  i.         none will graduate                                                 

 ii.        more than TWO (2) will graduate                                       

iii.       at least FOUR (4) will graduate                                                       

iv. the expected number of students that will graduate

Answer 1

This is a problem that is looking at probability of success or failure, so we use the Binomial Probability Function.

First let’s name some of the variables we are given:

X - This is our random variable which represents the number of students graduating

n = 10 the sample size

p = .40 the probability of success (students graduate)

q = .60 the probability of failure

Here we use the Binomial Probability Function:  

P(X = x) = _nC_x(p)^x(q)^n-x

i. P(X = 0) = ₁₀C₀(.40)⁰(.60)^10-0 = .0060

ii. P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + 

P(X = 9) + P(X = 10) = .2150 + .2508 + .2007 + .1115 + .0425 + .0106 + .0016 + .0001

= .8328

iii. P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + 

P(X = 10) = .2508 + .2007 + .1115 + .0425 + .0106 + .0016 + .0001 = .6178

iv. E(X) = np = 10(.40) = 4