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1.2. What if the result of the mammogram instead had been negative? Write out a table like Table 1.3 for a negative mammogram. What is the posterior probability that my friend will be diagnosed with breast cancer in this case? 1.3. What if the results of both the mammogram and the SCNB had been positive? Write out a table like Table 14 for a positive SCNB. What is the posterior probability that my friend has breast cancer in this case? 1.5. Suppose that three fair coins are flipped independently. What is the probability that exactly two of them come up heads?
Table 1.3 Bayes rule to go from prior probabilities to posterior probabilities Posterior Model Breast cancer No breast cancer Prior Probabilities Likelihood for M+ Prior x Likelihood Probabilities 0.0045 0.9955 0.724 0.0274 0.0033 0.0273 0.107 0.893
Table 1.4 Updated posterior probabilities Prior Probabilities for SLikelihood Probabilities 0.107 0.893 Likelihood Prior x Posterior Model Breast cancer No breast cancer 0.11 0.94 0.012 0.839 0.014 0.986
math   Statistics-And-Probability   
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15. Possible events in a sequence of flipping three coins: Sample space: Number events: n=cols (x) → 8 arHHH HHT HTH HTT THH THT TTH TTT] Event of interest or occurence of 2 heads: Ks HHT HTH THH] Number of events with 2 heads Expected Probability of 2 heads: Number of sequences Historical Probability: π- k-cols (K) → 3 P 0.375 =56 combin (n , k)=56 T:0.375Probability of getting the events of 2 heads with three coins will be binomially distributed with the probability is n-k -TK . (1-7) 0.2816 There will be 28.16% chance of finding the three events with two heads. There will 28 such sequences in 100 similar sequences.

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