Problem Set 9 hands? Probability X 9/1000 has finalphobia? 9/10 1/10 1/100 1/1000 9/100 992000 18012000 The probability that a person has finalphobia, given that he or she has shaky hands is Pr(F∩S Pr(Fis Pr(S) 9/1000 9/1000+99/2000 18+99 117 Problem 6. Outside of their hum-drum duties as 6.042 TAs, Ishan is trying to learn to levitate using only intense concentration and Grant is launching a Wang 2008" presi dential campaign. Suppose that Ishan's probability of levitating is 1 /6, Grants chance of becoming president is 1/4, and the success of one does not alter the others chances (a)If at least one of them succeeds, what is the probability that Ishan learns to levi- tate? Solution Let l be the event that Ishan learns to levitate, and let p be the event that grant becomes president. We can work out the desired probability as follows (L|(L∪P) Pr(L∩(LUP) Pr (LUP) Pr(∩P 1/6 1-(1-16)(1-1/4)= � � 8 Problem Set 9 has shaky hands? no yes yes no yes no 99/100 1/100 9/10 1/10 1/20 19/20 has finalphobia? F S X X 9/1000 1801/2000 99/2000 1/1000 Probability X X The probability that a person has finalphobia, given that he or she has shaky hands is: Pr (F | S) = Pr (F ∩ S) Pr (S) 9/1000 = 9/1000 + 99/2000 18 = 18 + 99 18 = 117 Problem 6. Outside of their hum­drum duties as 6.042 TAs, Ishan is trying to learn to levitate using only intense concentration and Grant is launching a “Wang 2008” presi￾dential campaign. Suppose that Ishan’s probability of levitating is 1/6, Grant’s chance of becoming president is 1/4, and the success of one does not alter the other’s chances. (a) If at least one of them succeeds, what is the probability that Ishan learns to levi￾tate? Solution. Let L be the event that Ishan learns to levitate, and let P be the event that Grant becomes president. We can work out the desired probability as follows: Pr (L (L ∪ P)) = Pr (L ∩ (L ∪ P)) | Pr (L ∪ P) Pr (L) 1 − Pr L ∩ P 1/6 = 1 − (1 − 1/6)(1 − 1/4) 4 = 9