Question

In a certain college, 33% of the physics majors belong to ethnic minorities. if 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Answer 1

To answer this question, we must first note that the probability of x successes in n trials is:

P = nCx*
`p^(x)`*
`q^(n-x)` where p and q are the probabilities of success and failure respectively.

In this case:

p = 33% = .33

q = .67

n = 10

x = 6

Calculating
`p^(x)`*
`q^(n-x)`:

`p^(x)`*
`q^(n-x)`=0.00026

Now the number of combinations of x in n trials is:

nCx =
`(n!)/(x!(n-x)!)`

Using the calculator to calculate for nCx from x= 1 to 6:

10C1 = 1

10C2 = 45

10C3 = 120

10C4 = 210

10C5 = 252

10C6 = 210

total nCx = 838

Substituting known values to the P equation:

P(6 or below are physics majors) = 838 * 0.00026

P(6 or below are physics majors) = 0.218