1) In a population of men, the probability that a man’s left eye is of brown colour is p, and the probability that a man’s right eye colour is brown is also p. Therefore the probability that a man has at least one eye of brown colour is: Pr(left eye brown or right eye brown) = Pr(left eye brown) + P(right eye brown) = 2p.
To be eligible for a certain type of manual work in the petroleum industry, a male must be above both a certain minimum height and a certain minimum weight. The separate probabilities that these are satisfied are ph (for height) and pw (for weight). Therefore for a man selected at random, the probability that he meets both criteria for the job is: Pr( Meets height and weight criteria) = Pr(Meets height criterion) x Pr(Meets weight criterion) = ph x pw
Suppose a student guesses the answers to three true/false questions. Whether the guess for any question is correct is independent of the guess for any other question being correct, and the probability of any guess being correct is 1=2. Overall, there are four possibilities for the number of questions the student guesses correctly, namely the student may guess 0; 1; 2; or 3 answers correctly. Therefore, because all four of these possibilities are equally likely, the probability that the student guesses all three questions correctly is 1=4.