A family thanksgiving dinner has 6 children and 6 adults present. The host unintentionally feeds the entire group a type of poisonous mushroom. This mushroom has a probability of .20 of making an adult sick, and probability .30 of making a child sick. Assume all the family members are independent regarding their reaction to the mushroom. What is the probability more adults get sick than children get sick. Let Y1 represent the number of children that get sick, and Y2 the number of adults that get sick. You should recognize the type of discrete random variables for Y1 and Y2. Then use the fact that Y1 and Y2 are independent. Solution more adults sick than children: cases: adult-1, child-0 Probability: 0.2*0.8^5*0.7^6 adult=2, child=0 or 1: probability:0.2^2*0.8^4*0.7^5 adult:3 child:0,1,2 probability: 0.2^3*0.8^3*0.7^4 adult:4,chuld:0,1,2,3 P = 0.2^4*0.8^2*0.7^3 adult:5,child:0,1,2,3,4 P = 0.2^5*0.8*0.7^2 adult:6,child:0,1,2,3,4,5 P=0.2^6*0.7.