DATI E PREVISIONI Indicating with Nk the event «k offsprings all black we have: 1 _ 1 1=_ p(N k) = _ 2k 2 2k+1 _1_ 1 ( ) male NN p N p NN | ( k ) 2k 2 p(male NN | N k) = __________________ = ________ = ______ k 1 p(N k) 2 +1 _1_ + ____ 2 2k+1 Since we want a confidence level greater than 95%, it must be: k 2 95 ______ > ____ k 2 +1 100 95 2k > ____ (2k + 1) 100 95 95 2k ____ 2k > ____ 100 100 5 95 ____ 2k > ____ 100 100 k > log 219 95 2k > ___ 5 95 95 2k (1 ____) > ____ 100 100 2k > 19 log19 k > _____ log2 k > 4,25 Since k is a natural number, it must therefore be k 5. At the fifth consecutive black pup, we can formulate the hypothesis that, with a confidence level greater than 95%, the male baby has the genotype NN. Questions 1 Is it possible to be sure of having a baby with the NN genotype? 2 Calculate what the minimum value of k must be to have the male with the NN genotype with a confidence level of at least 80%, 85% and 90%. 486