Bacteriophage P1 mediates generalized transduction in E. coli. A P1 transducing lysate was prepared by growing P1 phage on pur+ pro- his- bacteria. Genes pur, pro, and his encode enzymes required for the synthesis of purines, proline, and histidine, respectively. The phage and transducing particles in this lysate were then allowed to infect pur^ˆ’pro⁺his⁺cells. After incubating the infected bacteria for a period of time sufficient to allow transduction to occur, they were plated on minimal medium supplemented with proline and histidine, but no purines to select for pur⁺transductants. The pur⁺colonies were then transferred to minimal medium with and without proline and with and without histidine to determine the frequencies of each of the outside markers. Given the following results, what is the order of the three genes on the E. coli chromosome?

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Genotype Number Observed pro* bist 100 prot bist 22 prot his 150 pro bis