the addition law for events that are not mutually exclusive GCSE Statistics Probability the addition law for events that are not mutually exclusive

If events are not mutually exclusive, P(A or B) = P(A) + P(B) – P(A and B) This is the addition law for events that are not mutually exclusive. For example, in a group of people there are 5 men and 5 woman. Three of the men have red hair and one woman has red hair. If M stands for man and R for red hair: P(M) = 0.5 P(R) = 0.4 P(M and R) = 0.3 Then P(M or R) = 0.5 + 0.4 – 0.3 = 0.6

P(A U B) = P(A) + P(B) – P(A ∩ B) The notation in the text book is different P(A ∩ B) = P(A and B) ∩ means the intersection of the sets P(A U B) = P(A or B) U means the union of the sets the addition law is then written P(A U B) = P(A) + P(B) – P(A ∩ B) P(A or B) = P(A) + P(B) – P(A and B)

There are 800 children living in Finton There are 800 children living in Finton. 500 of the children have had chickenpox. One of the 800 children is chosen at random. A write down the probability that this child has had chickenpox P(C) = 𝟓𝟎𝟎 𝟖𝟎𝟎 = 𝟓 𝟖 =𝟎.𝟔𝟐𝟓 Some of the 800 children have had measles, M. A child is chosen at random. The probability that this child has had measles is 1 10 . B write down the probability that a child selected at random has not had measles. P(M) = 1 - 𝟏 𝟏𝟎 =𝟎.𝟗 Having measles is independent of having had chickenpox. C work out the probability that a child has had chickenpox, measles or both. P(C or M) = P(C) + P(M) – P( C and M) = 0.625 + 0.1 – (0.625x0.1) = 0.6625

Your turn Exercise 7I page 274