SOLUTION: A globe is spinning on a globe stand. The globe's surface is painted 30% yellow, 10% green, and the rest is painted blue. Two times Danny randomly points to a spot on the globe whi

Algebra ->  Probability-and-statistics -> SOLUTION: A globe is spinning on a globe stand. The globe's surface is painted 30% yellow, 10% green, and the rest is painted blue. Two times Danny randomly points to a spot on the globe whi      Log On


   

Question 1140032: A globe is spinning on a globe stand. The globe's surface is painted 30% yellow, 10% green, and the rest is painted blue. Two times Danny randomly points to a spot on the globe while it spins. The color he points to each time after the spinning stops is recorded. a) What is the probability that he points to the same color on both spins? b) What is the probability that he points to yellow at least one time?
Answer by ikleyn(52865) About Me  (Show Source):
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You are given 

    P(Y) = 0.3                    for yellow

    P(G) = 0.1                    for green

    P(B) = 0.6 (= 1 - 0.3 - 0.1)  for blue.


(A)  P = P(Y)*P(Y) + P(G)*P(G) + P(B)*P(B) = 0.3%5E2+%2B+0.1%5E2+%2B+0.6%5E2 = 0.46.     ANSWER


(B)  This probability is the probability to point to  

             (Y,G) or (G,Y);  

         or  (Y,B) or (B,Y);   

         or  (Y,Y), 


      and is equal thus to  2*0.3*0.1 + 2*0.3*0.6 + 0.3*0.3 = 0.51.    ANSWER