2.7 Laws of Probability

Ex 1 You are drawing cards from a standard deck. What is the probability that:

(a) you draw a 7 or a king?

(b) you draw a 7 or a heart?

Ex 2 (a) Prove that

(b) Does this formula work for all cases of A or B?

(c) How does the formula change if A and B are mutually exclusive events?

Ex 3 A box of chocolates contains 6 with hard centres (H) and 12 with soft centres (S). Calculate:

(a) P(H) (b) P(S) (c) (d)

Ex 4 In a class of 25, 14 students like pizza and 16 like iced tea, 1 student like neither and 6 like both. One student is randomly selected. What is the probability that the student:

(a) like pizza? (b) like pizza given that he/she likes iced tea?

Examining example 4 we can see that:

In 4b, if we know that the random student likes iced tea, then we can use the set I as our new sample space. Out of the 16 students who like iced tea, 6 like pizza. Therefore,

In general:

and so or

or

Ex 4 (c) likes iced tea given that he/she does not like pizza?

Ex 5 Bin A contains 3 red and 2 white tickets. Bin B contains 4 red and 1 white. A die with 4 faces marked A and 2 faces marked B is rolled and used to select bin A or B. A ticket is then selected from this bin. Determine the probability that:

(a) the ticket is red (b) the ticket was chosen from B given it is red?

(draw a tree diagram)

p. 486# 1-13

p. 490# 1-6