Math Analysis and Approaches

[Maximum mark: 6) In a class, 40 students take chemistry only, 30 take physics only, 20 take both chemistry and physics, and 60 take neither (a) Find the probability that a student takes physics given that the student takes chemistry. (b) Find the probability that a student takes physics given that the student does not take chemistry. (c) State whether the events "taking chemistry" and "taking physics" are mutually exclusive, independent, or neither. Justify your answer. [Maximum mark: 6] Two events A and B are such that P(A) = 0.25 and P(A U B) = 0.7. Find P(B), given that A and B are: (a) mutually exclusive; 121 (b) independent.(Maximum mark: 6) The events A and B are independent such that P(B) = 3P(A) and P(AUB) = 0.68. Find P(B) [Maximum mark: 4] (a) On the Venn diagram below, shade in the region A' UB'. E Two events A and B are such that P(A' U B') = 0.85 and P(B') = 0.6. (b) Find P(A ( B)[Maximum mark 14] UT Pablo drives to work The probability that he leaves home before 07:00 is Il he leaves home before 07:00 the probability he will be late for work is _ If he leaves home at 07 00 or later the probability he will be late for work is (a) Copy and complete the following tree diagram. [3] late before 07 00 not late late 07:00 or later not late (b) Find the probability that Pablo leaves home before 07:00 and is late for work [2] (c) Find the probability that Pablo is late for work [3] (d) Given that Pablo is late for work, find the probability that he left home before 07:00 [3] (e) Two days next week Pablo will drive to work. Find the probability that he will be late at least once [3]