Starter A school has 564 students 229 of

Starter A school has 564 students. 229 of them were absent for at least one day during Term due to sickness, and 111 students missed some school because of family holidays. 296 students attended every day of Term. What is the probability a student: ü Missed school for both illness and holidays ü Were away for holidays but not sickness ü Were absent during Term for any reason 72/ 564 39/ 564 268/ 564

Note 6: Types of Events Complementary Events If A is an event, then not A is the complementary event, written A′. Example: The probability a person passes Statistics is 0. 6. What is the probability a person doesn’t pass Statistics ? P(doesn’t pass Stats) = 1 – 0. 6 = 0. 4

Mutually Exclusive Events Mutually exclusive events cannot both occur. They have nothing in common. ie. No intersection. P(A U B) = P(A) + P(B) Example: In a pack of 52 cards, what is the probability that a card is chosen at random will be a heart or a club? P(heart or club) = P(heart) + P(club) =¼+¼=½

Independent Events When the occurrence of A has no effect on the likelihood of B occurring, the two events are independent. Examples: Are the following independent or not? üEvents A = {person has red hair) and B = {person passes Statistics exam) üEvents A = {person has done all revision supplied} and B = {person passes Statistics exam} The statistical definition of independent events is: P(A ∩ B) = P(A) x P(B)

Example: The probability an individual has blonde hair is 0. 5 and the probability an individual has blue eyes is 0. 3. The probability that an individual has blonde hair and blue eyes is 0. 21. Explain whether blonde hair and blue eyes are independent events. (BH ∩ BE) = 0. 21 (BH) x P(BE) = 0. 5 x 0. 3 = 0. 15 0. 21 ≠ 0. 15 Therefore, the events are not independent.

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