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(b) P(A U B) Recall the Addition Rule for two events, A and B, gives the probability of their union, P(A U B), as the following equation. P(A U B) = P(A) + P(B) - P(A n B) From part (a), we have the result P(A n B) = 0.05. We also have P(A) = 0.5 and P(B) = 0.1. Substitute these values into the Addition Rule above to calculate P(A U B). p(A U 3) = P(A) + P(B) P(A n B) o5+o1(E::::j) :l In a genetics experiment, the researcher mated two Drosophila fruit flies and observed the traits of 300 offspring. The results are shown in the table. Wing Size Eye Color Normal Miniature Normal 130 7 Vermillion 2 161 One of these offspring is randomly selected and observed for the two genetic traits. (Enter your probabilities as fractions.) (a) What is the probability that the fly has normal eye color and normal wing size? 13/30 J (b) What is the probability that the fly has vermillion eyes? 163/300 4 (c) What is the probability that the fly has either vermillion eyes or miniature wings, or both? 8/15 X A jar contains four coins: a nickel, a dime, a quarter, and a loonie. Three coins are randomly selected from the jar. (a) List the simple events in 5. (Use N for nickel, D for dime, Q for quarter, and L for loonie.) DQL, NQL, NDL, NDQ V (b) What is the probability that the selection will contain the loonie? (Enter an exact number as an integer, fraction, or decimal.) 0.75 (c) What is the probability that the total amount drawn will equal $1.30 or more? (Enter an exact number as an integer, fraction, or decimal.) 0.75 x The maximum patent life for a new drug is, in most cases, 20 years. Subtracting the length of time required by Health Canada for testing and approval of the drug provides the actual patent life of the drugthat is, the length of time that a company has to recover research and development costs and make a profit. Suppose the distribution of the lengths of patent life for new drugs is as shown here. Years,x 3 4 5 6 7 8 9 10 11 12 13 p(X) 0.02 0.05 0.07 0.10 0.14 0.24 0.15 0.12 0.07 0.03 0.01 (a) Find the expected number of years of patent life for a new drug. (Enter your answer to two decimal places.) 7.92 yr H (b) Find the standard deviation of X. (Round your answer to four decimal places.) 2.1104 V yr H (c) Find the probability that X falls into the interval )4 :t 25. (Enter your answer to two decimal places.) 0.01 X H