1. "53 Fever" The following account is based on a true story. In early 2005, Italy was in the midst of a mass hysteria concerning the number 53. It had been over 18 months since the number had come up in the country's national lottery. The media dubbed it "53 Fever." A woman drowned herself in the sea. A man shot his wife, child, and himself. Others went bankrupt, losing their life savings and their home. In one month alone, almost 700m ($711, 265, 738) was bet on number 53. The longer it went by without being called, the more convinced people became that it was due to show up and the more money they bet on it. The hysteria ended when the number finally came up in the February 9th draw in Venice after 182 no-shows and nearlyfour billion euros worth of bets. Assuming the lottery was fair, explain what was going on in light of what we have learned so far this term. What fallacy have these people committed? Include in your response terms suchas fair, unbiased, independent, and dependent.

2. "The Case of Sally Clark" The following account is based on a true story. In the fall of 1996, Sally Clark, an English solicitor (lawyer) in Manchester, gave birth to a baby boy. Eleven weeks later, he died. The following year she gave birth to another baby boy. Tragically, he also died, but when he was only 8 weeks old. The cause of death was unknown at the time, but the police suspected 'foul play.' Sally Clark was arrested and charged with two counts of murder. During the trial, her legal team argued that the children both died of Sudden Infant Death Syndrome, or SIDS, as it is commonly known. The prosecution's expert witness, Sir Roy Meadow, a famed pediatrician, testified that it was extremely unlikely that two children from an affluent family like the Clark's would die from Sudden Infant Death Syndrome. Meadow estimated that the odds of a single such case were 1 in 85,000. So, he reasoned, there was only a 1 in 73 million chance that the two deaths were "accidental." (85,000 x 2 = ~73 million.) That was apparently all it took to convince the jury. Clark was convicted of double murder and sentenced to life in prison. After three years in prison, Clark's lawyers were able to successfully overturn the casewhen it was discovered thatthe prosecution had withheld evidence pointing to the natural death of her second child. Clark, who had to deal not only with the loss of her two children but also a draining legal battle as well as the public scorn of being vilified as a child murderer, developed serious mental health problems. In March 2007, Sally Clark was found dead in her home fromalcohol poisoning.

What fallacy did both the prosecution and the jury commit in concluding that Sally Clark was guilty of murder? Include in your responseterms such as prior probability, conditional probability, and posterior probability.

Please separate the answers and explanations.