Scenario C (for questions 9-11): In the U.S., the probability of being male (assigned at birth) is 0.5. The probability of eating vegetables daily is 0.3 , The probability of being both a man and eating vegetables daily if 0.1. 9. What's the joint probability that we randomly select someone who is both male and eats their daily veggies? Show your calculation or explain where you got your answer with a drawing. a. 0.2 (b.) 0.1 c. 0.5 d. 0.3 e. None of the above 10. What's the conditional probability that someone eats their veggies daily given that they are male? Show your work. (a. 0.2 b. 0.1 (c.) 0.5 d. 0.3 e. None of the above P(AP)=P(B)(0,5,B) 11. What's the probability of randomly choosing someone who is either male or eats their veggies? Show your work. a. 0.3 b. 0.5 c. 0.7 d. 0.15 (e.) None of these.FORMULAS Joint pr, independent events pr(A,B)=p(A)p(B) Jointpr.dependenteventsp(A,B)=p(AB)p(B)=p(BA)p(A) Conditional probability (a rearrangement of the equation above) p(AB)=p(B)p(A,B) Union of two events p(AB)=p(A)+p(B)p(A,B) Law of total pt , version 1 B,dsp(E)=1 Law of total pr, version 2 p(notA)=1p(A) Permutations nPr=(nr)!n! Combinations nCr=r!(nr)!n! Z Score for sample Zi=syiy Z score for population Zi=yi Raw value given a z-score yi=(sZ)+y Binomial approximation to normal distribution z-score z=np(1p)(x.5)np.