Answer:
30% probability that Joe is among the chosen students.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the students are chosen is not important, so the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
Joe
14 remaining students, from the remaining 49. So
[tex]D = C_{49,14} = \frac{49!}{14!(49-14)!} = 675248872536[/tex]
Total outcomes:
15 students, from a set of 50. So
[tex]T = C_{50,15} = \frac{50!}{15!(50-15)!} = 2.2508296 \times 10^{12}[/tex]
Probability
[tex]p = \frac{D}{T} = \frac{675248872536}{2.2508296 \times 10^{12}} = 0.3[/tex]
30% probability that Joe is among the chosen students.
