The following table shows 1000 nursing school applicants classified according to scores made on a college entrance examination and the quality of the high school from which they graduated, as rated by a group of educators:

Quality of High Schools Score Poor (P) Average (A) Superior (S) Total Low (L) 105 60 55 220 Medium (M) 70 175 145 390 High (H) 25 65 300 390 Total 200 300 500 1000

(a) Calculate the probability that an applicant picked at random from this group:
Made a low score on the examination.
Graduated from a superior high school.
Made a low score on the examination and graduated from a superior high school.
Made a low score on the examination given that he or she graduated from a superior high school.
Made a high score or graduated from a superior high school.

(b) Calculate the following probabilities:
P(A) 2.

P(H) 3.

P(M)

PðA j HÞ 5.

PðM \ PÞ 6.

ðH j SÞ