Question

5. Based on a survey, 39% of the respondents feel guilty about wasting food, 27% of the respon- dents feel guilty about leaving lights on when not in a room, and 12% of the respondents feel guilty for both reasons. (a) (5 points) What is the probability that a randomly selected person feels guilty for either wasting food or leaving lights on when not in a room? (b) (5 points) What is the probability that a randomly selected person does not feel guilty for either of these reasons? 6. Suppose a fair coin is tossed three times (a) (5 points) What is the number of possible outcomes of this experiment? Explain your answer (b) (5 points) List all the outcomes of this experiment. (c) (10 points) Given that you have observed at least one heads, what is the probability that you observe at least two heads?

Answer 1

5. - A - Feet guilty obowl wasting feed. B- feel guilty about leaving lights on Given, .P (A) = 0.39 P(B) = 0.27 PLANB) = 0.12 © PLAUB) = PTAI + P (B) – PIA OBD = 0.39 +0.27 -0.12 = 10.54

0 PLAUB) = PlanBjC =1-PRAMB) 51 -0.12 = 10.887 There are two outcomes & Head (H), Tails (T)} for a Coin toss. Since, we are tossing it three times - 2x2x2 = 8 outcomes are possible. - s ={HHH, HHT, HTU, HTT, THI, ITH THT, TTT? © P(x2721x21) = P(x22,X>1). P(x21) = P(x72) = .4/8 14 P(*71) 7/8 17