11-12. Assume that in STT 201, 60% of all students are females. A random sample
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11-12. Assume that in STT 201, 60% of all students are females. A random sample of three students is drawn one-by-one 11. What is the probability that only the first two students are females? (a) 0.125 (b) 0.144 (c) 0.375 (d) 0.432 (e) 0.360 12. What is the probability that two of three students are females? (a) 0.125 (b) 0.144 (c) 0.375 (d) 0.432 (e) 0.360 13-14. An urn contains 2 blue and 3 green balls. Three balls are drawn at random without replacement. Let b denote a blue ball and g denote a green ball. 13. Use the multiplication rule to find the probability of the (ordered) outcome of bgg (a) 0.450 (b) 0.144 (c) 0.150 (d) 0.432 (e) 0.200 14. The probability of selecting one blue ball and two green balls is: (a) 0.450 (b) 0.144 (c) 0.150 (d) 0.432 (e)0.600Explanation / Answer
11. Probability that the first student is a female = 0.6
Probability that the second student is a female = 0.6
Probability that the third student is a male = 0.4
=> Probability that only the first two students are female = 0.6 * 0.6 * 0.4 =0.144.
12. We have seen that the probability of first two students only being female = 0.144.
Two females can be chosen out of 3 in 3C2 = 3 ways.
=> Probability that two students are female = 3*0.144 = 0.432.
13. Blue ball can be drawn in 2 ways.
The first green ball can be drawn in 3 ways and the second in 2 ways.
Totally, three balls can be drawn in 5P3 = 60 ways.
Probability = 2*3*2/60 = 1/5 = 0.200.
14. We saw that the probability that the first ball is blue and the next two are green is 0.2.
Similarly the probability will be 0.2 if the blue ball is second or third.
Total probability = 0.2 + 0.2 + 0.2 = 0.600.
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