Question

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Probability Theory (40 pts) 1. (20 pts) Suppose that you obrved the last two days and found the probability of your feeling "bad" (B) when waking up is 0.2, the probability of feeling'okay" (O) is 0.3, and the probability of feeling 'wood' (G) is 0.5. Find the probability of feeling good on at least one day. (a) Find the sample space S. (5 pts) (b) Find the probability for each outcome of S. (5 pts)

Answer 1

Given PCB 0 2 P(O) = 0.3 PCG) :05 We are considering two consecutive days Cherefore she possible ou on these days are the following possible ouhomes (a) Sa Sample space BB , BO, BA 100,0B, OG GG , GO GB? 9 Probability 9 feeling good on atleast one day - P BG OP OG OF GG or Goor GB = PCBG) + PCOM) + P(46) + PCGO) + P(GB) : 02x0.5 +0.3x05 +05X06* 0.5 x 0.+ 0.5X0.2 - 01 + 0.15 +0.95 +0.15+0.1 = 0.15 day j and day & are independent .. to each since other. feeling of on b) PCBB) - PCO).PCB) - 0.2 x0.2 -0.04 PCBO = P(0) - POPCO) = 0.2x0.3 - 0.06 PCBG) - P(46) - PCC).PCB) = 0.2X0.5 = 0.10 pCoo) : PCO).PC) -0.3x0.3 -0.09 P (OG) - P(90) - PCG) (0) 0.5 0.% = 0.15 P COG) - PC4).P(G)-0.5*0.5 = 0.96 c) sebe A = { BG ,09, GG,G,@, GB) PC) = 0.15