Please show all work. 1. Suppose a lbox coutains 4 identically-sized balls numbe

Question

Please show all work. 1. Suppose a lbox coutains 4 identically-sized balls numbered 0. 1. 2, and 3. We perform a rauwlom experinment by drawing two balls at random from the box without replacement and way. Note, the "ordered way" means (a, b) (6a) putting those in an ordered for an event where a.b are any two uumbers among 0. 1, 2, aad 3 (a) (5 points) State the sample space, S. (Ib) (5 points) Let A be the event that the ball mmbered 3 is drawn and B be the event that the stun of the munbers in the two balls that are drawn is at nost 4 Calculate Pr[Al and PriB (e) (5 points) Calenlate PrLALB)

Explanation / Answer

1:

(a)

Since balls are drawn without replacement so possibe number of outcomes are 4 *3 = 12. Possible sample space is

S = { (0,1), (0,2), (0,3), (1,0), (1,2), (1,3) , (2,0), (2,1), (2,3), (3,0), (3,1), (3,2)}

(b)

Out of 12 outcomes, 6 outcomes have ball numbered 3 so

P(A) = 6/12 = 0.5

Out of 12 outcomes, 10 outcomes have sum 4 or less so

P(B) = 10 /12 = 0.8333

(c)

Out of 12 outcomes, 4 outcomes have sum at most 4 and have a numbered 3 ball so

P(A and B) = 4/12

Therefore:

P(A|B) = P(A and B) / P(B) = (4/12) / (10/12) = 0.40

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