PLEASE HELP ME SOLVE and EXPLAIN PROBLEM #2, SET \"A\" AND \"B\" PLEASE! Among 3

Question

PLEASE HELP ME SOLVE and EXPLAIN PROBLEM #2, SET "A" AND "B" PLEASE!

Among 33 students in a class, 17 of them earned A's on the midterm exam, 14 earned A's on the final exam, and 11 did not earn A's on either examaination. What is the probability that a randomly selected student from this class earned an A on both exams? Let A and B be two events. The event (AB) union (BA) is called the symmetric difference of A and B and is denoted by A angle B. Clearly, A angle B represents the event that exactly one of the two events A and B occurs. Show that P(A angle B) = P(A) + P(B) - 2P(A intersection B).

Explanation / Answer

a ans) No of students who earned A's in either of the exams = 33-11 =22 .
      , No of students who earned A's in both the exams = 17+14-22 = 9

hence Probability of a randomly selected student earning A's in both exams is 9/33 =3/11

bans) A U B = (A n B) U (A n B’) U (A’ n B)

P(A U B) = P(A n B) + P(A n B’) + P (A’ n B)

+P (A n B) - P (A n B)

= P(A)+P(B)-2 P(A n B)

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