Question

Example. 2 urns. Red urn contains 3 red balls, 2 white balls. White urn contains 1 red ball, 4 white balls. Pick an urn randomly. Randomly select a ball from that urn. Without replacing the 1st ball, select a ball from the urn whose color matches the first ball. Q. Make a tree diagram, complete with probabilities describing this situation. Q. Find the probability that the first ball is white. Q. Find the probability that the second ball is white. Q. Find the probability that the red urn was picked given that both balls are white. SECTIONS 2.3, 2.4.2.5, 2.6

Answer 1

Let's define the events urn} Red = { Red urns, white = { white P(Red urn is selected) = P( White un is select) = 2 R = { Red ball is select} we { white ball is select} Let's make tree diagram from the given information. 315 o 214 OR 112 2 uzred 2/5 W 114 i Red 2/5 white 415 Note: Suffin is denoted for number of draws Q.2 pl first ball is white) = P(WI) 6.3 = P( Red and w) + P( White and w) = } << + * { = t = 0.7 P( second ball is white) = P(W21R., Red) + P(Wq 1Wi, to Red) + P (W2 | Ry, white) + P(uz 1 BW, white) P(W2) = (1-2) 3 + + 2 k + (1-0) } £ + 2 2 3 3 £ P(W) = a 6+2+4+ 12 – 24 = = 0.60 = 6 - = 24 4x10 4*10

8.4 Here we want to find P (Red I w, wa) = P(Red, W,,W2) PCW,,일) 글중국 을름차글송을 120 Yoo + 120 P(Redw,l= ㅗ 09