Answer:
(a) 0.4 (b) 0.067 (c) 0.53 (d) 0.44; 0.11; 0.45
Step-by-step explanation:
(a) In this part, you like 4 out of 6, the probability of choosing one at random will be 4/6 = 2/3. If you choose another one at random, the probability will be 3/5. Thus, P(like both) = (2/3)*(3/5) = 0.4. No, because it is above 0.05.
(b) The probability that you do not like a random selection is 2/6. The probability that you do not like the second random selection is 1/5. The probability of not liking both will be (2/6)*(1/5) = 0.067
(c) Based on the available options that are like both, do not like both, and like only one, we can deduce the probability of liking exactly one as:
1 - P(like both) - P(like neither) = 1 - 0.4 - 0.067 = 0.53
(d) If the songs can be repeated:
P(like both) = (2/3)(2/3) = 0.44. It is not unusual because it is more than 5%.
P(like neither) = (2/6)(2/6) = 0.11
P(like exactly one) = 1 - 0.44 - 0.11 = 0.45
