Algebra 2 Word Problem Help

Question

The principal will randomly choose 6 students from a large school to represent the school in a newspaper photograph. The probability that the chosen student is an athlete is 30% (assume that this does not change). Round to the nearest thousandth.

 

What is the probability that 4 athletes are chosen?

 

What is the probability that at least 4 athletes are chosen?

Answer 1

This is called a Bernoulli experiment or a binomial experiment. Do you understand the binomial theorem? I hope so because that's what I use to explain this.

 

Let A = probability of athlete and N = non-athlete. Note N + A = 1. So in your case, N = .3 and A = .7

 

Since you need 6 people you have the following situation.

(A+N)(A+N)(A+N)(A+N)(A+N)(A+N)

 

You need 4 As and 2 Ns for your group of 6. But you don't know which of the 6 sets of parenthesis will be the A's.

So,

₆C₄ * A⁴*N² = 15*(.3)⁴(.7)² = .059535 round to the thousandth = .060

 

 

The next part of the question involves exactly 4 athletes, exactly 5 athletes, and all athletes.....then add them up.

 

Hope this helped.