Probability Questions

Question

In a high school mathematics exam, 72% of the students score grade B and below while the remaining 28% score A. Among those students who score grade A, 23% are female while 53% of the grade B and below students are female.

Let R= students who score B or lower ; L= students score A ; F= student is female. A student is selected randomly from the class.

a) Calculate the probability that the student is female.

b) Is L independent of gender?

c) Given that the student selected is female, calculate the probability that she is scoring B or lower.

Please help me with this questions :(

Answer 1

As:

28% Overall

23% Female

77% Male

Bs and Lower

72% Overall

53% Female

47% Male

R = 72% the percentage of students who scored a B or lower

L = 28% The percentage of students who scored an A

F = Female student.

a.) P(F) is the probability that a student is female. We need the female portion that scored As and the portion that scored Bs or lower

P(F) = 23% of 28% + 53% of 72% or,

P(F) = .23 x .28 + .53 x .72

b.) P(L) = 28%. The event that we choose a student who scored an A is independent of their gender.

c.) Conditional Probability, what is the probability a student selected is Female (F) given they score B or lower (B)

P(F | B) = P(F and B) / P(B)

What is the probability that student is female and scored a B or lower?

What is the probability the student scored a B or lower?

Identify these percentages from the given values and divide.