SOLUTION: 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

Question 1171367: 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.
i) Calculate the probability that the student is female.
ii) Is L independent of gender?
iii) Given that the student selected is female, calculate the probability that she is scoring B or lower.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Look at 100
=======L===== R=====Total
M------21.56----33.84---55.4
F-------6.44-----38.16---44.6
Total---28-------72-------100
Randomly from the class, 0.446 probability female
-
P(M)*P(L) should equal P(M&L)
0.155 should equal 0.2156. They do not.
Score is not independent of gender
-
Given female (44.6), 38.16 were R for 0.8556 probability.

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