Question
all tables are numberd from 1-30
equation p(a) stats-Goc × a/moodle/pluginfile.php/2215664/mod_resource/content/1/STAT2507.Asst2.517.pdf n A Company G Google justification. PART AtEstimating Probabilities 1. Consider 16 ping-pong balls which are classified aocording to their collour (white, yellow, and orange) and the eolour of the dots ( blue and red) on them, so every ball, regardless of color, has a mar . blue dot. The distribution of the halls over these catrgorics is summarized in the following contingency table: 1 1 | white (W) Yellow (Y) Orange (0) Total Red Dot (R) a) Suppose that one of the 16 bails is sclected at random, Let W be the event the ball is White, and B be the event the ball has a bloe dot What is the probability that i) the ball is white,P(wy i) the ball has a blue det, P(By ni) the hall is white and has a blue dot, P(WnB iv) the ball has a blue dot given it is whine, PlBWy? v) the ball is whine given it has a blue dot, Piway b) Table A records the sumber of oecurences of W. B, wnB in n daws(with replacement) fhom a bos containing all 16 balls. For this small number of qplications, what are the relative frequencies of. ) balls that are white, P(wy? ii) balls that have a blue dot, P(B)? iii) halls that are white and have a blue da, (w n i)? Note the #" symbol denotes that the relative freqemcies are only estimates of the actual peobabilituies v Compare the relative frequencies in i, ii), n) with the t correspoading thooectical prohabilaies fecenm partia) c,(, Ase the close? Explain e) Table B reconds the numsber of talls with blue dots that were obtained in n seplications of drawing a ball from the bos of 8 whine halls. a) Compare the relative frequency. P(Blw), to the theoretical peobabulity,PYW di Tahle C records the number of white balls obsainod in a replications of drawing a ball from the bos ofs balls with bloc dets 1) Compare the rellivelrequency. (wis), lo she theorewal perhahilily, I'w1131, OMP
Explanation / Answer
a)
i)
P(W) = 8/16 = 0.5
ii)
P(B) = 5/16 = 0.3125
iii)
P(W and B) = 2/16 = 0.125
iv)
P(B|W) = P( B and W)/P(W) = 0.125/0.5 = 0.25
v)
P(W|B) = P( B and W)/P(B) = 0.125/0.3125 = 0.4
