statistics1. (7 points) The following is known. 2% of women have breast cancer. 80% ofmammograms detect breast cancer when it is there (and therefore 20% miss it).9.6% of mammograms detect breast cancer when its not there (and therefore90.4% correctly return a negative result).a) A woman was picked randomly was given a mammogram test. What is theprobability that she will be tested positive?b) Suppose she was tested positive. What is the probability that she actuallyhas breast cancer?2. (7 points) A shipment of 25 items contained 5 defectives. The buyer tested 7randomly selected items from the lot.a) What is the probability that she will find exact two defectives in the sample?b) What is the probabilility that she will find at least one defective in thesample?3.183 Series and parallel systems. Consider the two systemsshown in the schematic on page 174. System A operatesproperly only if all three components operate properly.(The three components are said to operate in series.) Theprobability of failure for system A components 1, 2, and 3 is12, .09, and .11, respectively. Assume that the componentsoperate independently of each other.174 CHAPTER 3 ProbabilitySystem A: Three Components in SeriesInput ->.-‘.-.-’ OutputSystem B: Two Parallel Subsystemso Subsystem C QInput –< -* OutputSubsystem DSystem B comprises two subsystems said to operate in a. It is known that the proportionsparallel. Each subsystem has two components that operate produced by the seven suppliein series. System B will operate properly as long as at least .006, .0002, .0002, and .001, respone of the subsystems functions properly. The probability microchip failure is observed,of failure for each component in the system is .1. Assume likely responsible?that the components operate independently of each other. b. Suppose the seven suppliers pra. Find the probability that System A operates chips at the same rate, 9005, IfP1“ OPCT lY- failure is observed, which suppli-b. What is the probability that at least one of the compo- sible?t’ St Awillf’l dth f thtth t3 fsalilllq ys em a1 an ere ore a e sys em *3.186 Dream experiment in psychologc. Find the probability that System B operates properly. ‘3 glst ls grvg: tapes if 120 $113)]?th(1. Find the probability that exactly one subsystem in reams. . .e . psyc 0 ong ls 0System B fails anx1ety 1nd1v1duals and 10 are 10e. Find the probability that System B fails to operate Elijfcsgmdogm S task 1s to seleproperly.f. How many parallel subsystems like the two shown here 3’ Count the number of samplewould be required to guarantee that the system would ment.operate properly at least 99% of the time? b- Assuming that the PSYChOIOEISt