Question

A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.

Answer 1

Step-by-step answer:

Use conditional probability.

P(A|B) = P(A intersect B) / P(B)

= probability of A given B is true (or has happened)

Here,

A = athelete, P(A) = 10/40

B = honours student, P(B) = 11/40,

P(~B) = 1-11/40 = 29/40

Of the 10 atheletes, 3 are also honours students.

Therefore there are 7 atheletes who are NOT honours students.

P(A and ~B) = 7/40

Therefore

P(A|B) = P(A and ~B) / P(~B)

= (7/40) / (29/40)

= 7/29