In an exemingtion, the pobabilinies of cheled Scaing the heigegt mevic in Mathem onics, Playsid and Clemisty ave $0.90,0.75$ and 0.80 vespectively. calc. The puobchility that Le Dill qet the heizeff mank in
icll the 3 abjeti
iो at leart 2 sicsjets
Answer
Calculate the probability of Scaing the heigegt mevic in at least 2 subjects: \(P(A \cap B) + P(A \cap C) + P(B \cap C) - 2P(A \cap B \cap C) = P(A)P(B) + P(A)P(C) + P(B)P(C) - 2P(A \cap B \cap C) = 0.90 \times 0.75 + 0.90 \times 0.80 + 0.75 \times 0.80 - 2 \times 0.54 = \boxed{0.765}\)
Step 1 ：Let A, B, and C be the events of Scaing the heigegt mevic in Mathematics, Physics, and Chemistry respectively.
Step 2 ：Calculate the probability of Scaing the heigegt mevic in all 3 subjects: \(P(A \cap B \cap C) = P(A)P(B)P(C) = 0.90 \times 0.75 \times 0.80 = \boxed{0.54}\)
Step 3 ：Calculate the probability of Scaing the heigegt mevic in at least 2 subjects: \(P(A \cap B) + P(A \cap C) + P(B \cap C) - 2P(A \cap B \cap C) = P(A)P(B) + P(A)P(C) + P(B)P(C) - 2P(A \cap B \cap C) = 0.90 \times 0.75 + 0.90 \times 0.80 + 0.75 \times 0.80 - 2 \times 0.54 = \boxed{0.765}\)
