Question

a to d

Problem 6 10 points Consider the following simple lottery game. There are ten balls total of which five are red and numbered 1,2,3,4,5. The remaining five are blue and also numbered 1,2,3,4,5. Three balls are simultaneously pulled out from a hat, and depending on what they are, you might win a prize. (a) You win a teddy bear if all three balls are the same color. What is the probability of winning a teddy bear? (b) You win a baby Yoda figurine if the three balls have consecutive numbers (such as red 2, blue 3, and blue 4) regardless of color (or order). What is the probability of winning a baby Yoda? (continued on next page)

Answer 1

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@D(teddy bear)- Plau Bare Red)+ P(all 3 are blue) 6)+(3), (1. 6 If no are consecutive, they can be (1,2,3), (2,3,4) Dr(3,4,5). Also for each of 3 no we have a possibilities, red or blue. So, favourable ways= 3 * 2*22= 24 P(win a bir.figurine) = 2 = 1 + 3) = 0.2 © det x: No of times you win Baby Vodas. Xu Bin(4,0.2) 2) PEX-3): () (0.237(1-0,2)*-* P(x>,3)=)(0.23(0.8)+ (%)(0.23 -10.0272) @det A and B be the event of winning a teddy bear & a Baby Voda respectively, P(A)= VPCB): 15 P(ANB) = Plall 3 are same color & consecutive) €3+3=6 ways] = 6/(19) - 0.05 - Yo . PlA or B) = P(A)+ PCB)- P(ADB) = + 6 + +5 - 20 = 19 = 10.3167]