Some information regarding the composition of the student athlete population in

Question

Some information regarding the composition of the student athlete population in a high school is given in the table below. For example, 65% of the student athletes are male, 50% of student athletes play basketball, and female athletes do not play football. For a student athlete selected at random, the events F={ the student athlete is female } and T={ the student athlete prefers track are independent. Football Basketball Track Total 0.65 Male Female Total 0.3 0 0.3 0.5 0.2 (a) Fill in the reaming entries of the above table. (b) If a randomly selected student athlete prefers basketball, what is the probability that the student athlete is female? (c) Are the events F and B- the student athlete prefers basketball ndependent?

Explanation / Answer

for P(F) =1-P(Male) =1-0.65 =0.35

P(T) =0.2

as F and T are independent ; therefore P(F nT) =P(F)*P(T) =0.35*0.2 =0.07

hence from given data:

b)

P(female|basketball) =0.28/0.5 =0.56

c)

as P(FnB) =0.28 while P(F)*P(B) =0.35*0.5 =0.175

as they both are not equal ; therfore F and B are not independent.

football basketball track total male 0.3 0.22 0.13 0.65 female 0 0.28 0.07 0.35 total 0.3 0.5 0.2 1

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.