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
Answer:
(a) 0.3084
(b)0.6916
(c)0.3394
d 0.2804, 0.7196, 0.3856
Step-by-step explanation:
p=4/15, q= 1 - 4/15=11/15
(a) n= 2 , x = 2.
We use the Bernoulli random distribution formula.
P(X= 2) = 6C2(4/15)²(11/15)⁴
=15 ×0.0711 × 0.2892
= 0.3084
(b) Pr(X=2) + P(X=2)' = 1
P(X=2)' = 1 -P(X=2)
= 1 - 0.3084
= 0.6916
(c) n= 6, X=1
Pr(X=1) = 6C1 (4/15)¹(11/15)^5
= 6 × (4/15) × (11/15)^5
= 6 × 0.2667 × 0.2121
= 0.3394
(d) This means only 5 is replayes in the random order.
d(a) n= 5, X= 2
Pr(X=2) = 5C2(4/15)²(11/15)³
= 10 × 0.0711× 0.3944
= 0.2804
d(b) Pr(X=2) + P(X=2)' = 1
P(X=2)' = 1 - 0.2804
P(X=2)' = 0.7196
d(c) Pr(X=1) = 5C1 (4/15)¹(11/15)⁴
P(X=1) = 5 × 0.2667 × 0.2892
= 0.3856
