Cereal Character Cosmic Crisps Intergalactic Granola Resistance Rice Flakes All BB& 70 105 70 245 C-3PO 40 180 25 245 Chewbacca 65 55 80 200 Finn 50 30 75 155 Rey 75 30 50 155 All 300 400 300 1000 (b) Suppose you randomly select one box of cereal from this shipment. What is the probability that the prize is the character C-3PO? Use probability notation. You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(CP)= 245/1000=.245 (c) Suppose you randomly select one box of cereal from this shipment. What is the probability it is not Cosmic Crisps? Use probability notation. You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(CC)=300/1000=0.3= 30% P(CC )= 1-P(CC)=1- (300/1000)= 0.7=70% (d) In case you do not follow the Star Wars Movies, Rey and Finn are humans, Chewbacca is a Wookie, and BB8 and C3PO are droids (robots). What is the probability of selecting a random box of cereal that is Intergalactic Granola and contains a droid? Use probability notation. You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) D=Droid (bb8 & c3po) P(I and D)= P(InD)= P(1)*P(D|I) P(1)= 400/100=0.4 P(D | 1)= P(DnI)/ P(1)[ (105+180)/1000 ]/ (400/1000) =0.7125 P(InD)= 0.4*0.7125= 0.285= 28.5% Or just solve simply- P(InD)= 285/1000= 28.5% (e) What is the probability of selecting a random box of cereal that is Intergalactic Granola or contains a droid? Use probability notation. You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(I or D)= P(IUD)= P(I)+P(D)-P(InD) =(400/1000)+ ((245+245)/1000)- ((105+180)/1000) P(IUD)=0.605=60.5% (f) Given the event that you selected a box of Intergalactic Granola from the shipment, what is the probability that your prize is the character C-3PO? Use probability notation. You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(CPI)= [P(CPI)]/P(I)=0.45=45% (g) Suppose that your favorite character is Chewbacca the Wookie. Which cereal type should you select in order to have the highest probability of obtaining a Chewbacca toy? Justify your answer using probabilities numerically. An intuitive description without using probabilities won't receive any credit. Using probabilities without showing their numerical values won't receive full credit. (5 points) Cosmic= 65/300=0.21667=21.67% Intergalactic= 55/400=0.1375= 13.75% Resistance= 80/300=0.26667= 26.67% The resistance rice flakes have the highest probability of containing a Chewbacca toy.(h) Are the events selecting a box of Intergalactic Granola and getting the character C-3PO as the prize independent? Justify your answer using probabilities numerically. An intuitive description without using probabilities won't receive any credit. Using probabilities without showing their numerical values won't receive full credit. (Hint: Use a test for independence.) (5 points) P(InCP)=P(I)*P(CP) 180/1000 =(400f1000) * (245/1000) 0.13 = 0.098 -NOT EQUAL so NOT INDEPENDENT AT 3090 LAB S: PROBABILITY FALL 2022 (i) Select two events from this table that you believe are mutually exclusive. Justify your answer using probabilities numerically. An intuitive description without using probabilities won't receive any credit. Using probabilities without showing their numerical values won't receive full credit. (5 points) Event 1 probability select intergalactic cereal= P(I) Event 2- probability select resistance cereal= P(R) P(InR)=