Question 1 (a) Given that the probability that an archer hits the target with ea

Question

Question 1 (a) Given that the probability that an archer hits the target with each arrow he shoots is 0.85. The archer shoots arrows repeatedly until he hits the first target. What is the expected value number of arrows he shoots? (i 0.8 i 0.6 (iv) 1.5 (b) The ticket machine in a car park takes 50 cent coins and $1 coins. A ticket costs $1.50 The probability that the machine will accept a particular 50 cent coin is 0.9 and that it will accept a particular $1 coin is 0.8 Mary puts one 50 cent coin and one $1 coin into the machine What is the probability that the machine will not accept either of these coins? (i)0.02 (ii) 0.72 (iv) 0.98 (c) A history of 266 air samples has been classified on the basis of the presence of two rare molecules. Let A denotes the event that consists of all air samples in which rare molecule 1 is present. Let B denotes the event that consists of all air samples in which rare molecule 2 is present. Find the probability: P(molecule 2 present molecule 1 present) ?Molecule 1 present? Yes Molecule 2 present No 212 24 Yes 18 12

Explanation / Answer

a. p = 0.85 + 0.15(0.85) +0.15*0.15(0.85) ....... = 0.85 (1 + 0.15n ) , where n tends to infinity

P(X=1)=p=pq0=0.85

P(X=2)=qp=pq1=0.15 * 0.85

E(X)=n=1 = npqn1=1 / p = 1/0.85 = 1.2

b. probability that the machine will not accept any coin = (1-0.1 ) * (1-0.2) = 0.02

c

P(A) = (24+12)/266

P(B) = (18+12)/266

P(A and B) = 12/266

P(A|B) = P(A and B) / P(B) = (12/266) / ( 30/266) = 12/30 = 4/10 = 0.4

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