At 3:00 am this morning, a first-year student at UTS named Benjamin reported to the police at the Merrylands Police Station that he was mugged. He said that he was walking home in the Merrylands suburb of Sydney, when suddenly he was grabbed from behind and pinned to the ground by his attacker. He struggled violently to try to free himself but couldn't. His attacker took his wallet and mobile phone out of his back pants pocket, and finally, after what seemed like several minutes, let him go and ran away. This occurred at around 2:30 am. Benjamin was unable to provide any description of his attacker. Benjamin was wearing a white, sleeveless shirt and grey pants. His bare arms were taped to recover fiber evidence. The police investigation considers the attacker to be someone in Sydney. A few hours later, Mr. A came to the attention of the police in relation to this case. The police confiscated Mr. A's long-sleeved, hooded top. ITEMS: adhesive tape liftings from Benjamin's bare arms reference fibers from Benjamin's cloths Mr. A's long-sleeved hooded top QUESTION: Did Mr. A mug Benjamin? METHODS: The tape liftings on Benjamin's arms were conducted using high-adhesive, J-LAR, 72 N/25 mm, 2 cm wide tape, which was then attached to transparent A5 acetate sheets. These were examined using a low-power Nikon SMZ645 stereomicroscope to localize fibers, and with a high power brightfield and polarized light microscope to identify the generic class and color of fibers. The color of the fibers was identified using the microscope's transmitted light mode. Any fibers similar to the reference fibers from Benjamin's cloths were ignored. The remaining fibers were counted. The fiber sheddability of Mr. A's hooded top was determined. Then a set of reference fibers were taken from Mr. A's hooded top and examined using a high power brightfield and polarized light microscope. The generic class and color were determined. These fibers were then compared with any similar fibers found on the tape liftings of Benjamin's arms. RESULTS: The tape liftings from Benjamin's arms contain 177 foreign fibers (i.e., fibers different from the reference fibers taken from Benjamin's clothes). These were identified as blue, cotton fibers. Mr. A's hooded top has high fiber sheddability. It is made from 100% cotton fibers of the color blue. The 177 blue, cotton fibers recovered from Benjamin's arms are indistinguishable from the fibers of Mr. A's hooded top. According to an in-house study conducted at this forensic science laboratory, the probability of finding zero groups of foreign fibers on a person's arms by chance is 0.2, and the probability of finding one large group (i.e., > 100 fibers) of foreign fibers on a person's arms by chance is 0.1. According to the results of the following study: Watts R., Roux C., Robertson J. The population of coloured textile fibres in domestic washing machines. Science & Justice 2005; 45: 75-83. the probability of someone wearing a blue cotton top during spring in Sydney is 0.2.

The goal of this is to determine the likelihood ratio.