If an urn contains 3 white and 4 black balls and if balls are randomly drawn wit
ID: 2930229 • Letter: I
Question
If an urn contains 3 white and 4 black balls and if balls are randomly drawn without replacement, answer the following, each as a separate drawing. 10.1 In drawing two balls, determine the probability of drawing one white and one black 10.2 In drawing two balls, determine the probability of drawing one white and one black ball in that order 10.3 In drawing three balls, identify all the possible outcomes color-wise 10.4 Assuming two identical urns and assuming two balls are drawn from each urn, determine the probability that one urn will yield in one white and one black ball, order unimportant, and the other urn will yield something else.
Explanation / Answer
Given: An urn containing 3 white and 4 black balls and balls are drawn without replacement.
10.1 To get: probability of drawing one white and one black
Probability of getting white ball in 1st draw=3/7
Probability of getting black ball in 2nd draw=4/6
Similarly;
Probability of getting black ball in 1st draw=4/7
Probability of getting white ball in 2nd draw=3/6
Therefore, probability of drawing one white and one black ball= (3/7)(4/6)+(4/7)(3/6)= 0.5714
10.2 Probability of drawing one white and one black ball in that order= (3/7)*(4/6)=0.2857
10.3 In drawing three balls, probability of all the possible outcomes color-wise
All the possible combinations are: www, wwb, wbw, wbb, bww,bwb, bbw, bbb
So, probability of all the possible outcomes color-wise is => P(www)= (3/7)(2/6)(1/5)=0.0286
P(wwb)= (3/7)(2/6)(4/5)=0.1143
P(wbw)= (3/7)(4/6)(2/5)=0.1143
P(wbb)= (3/7)(4/6)(3/5)= 0.1714
P(bww)= (4/7)(3/6)(2/5)= 0.1143
P(bwb)= (4/7)(3/6)(3/5)=0.1714
P(bbw)= (4/7)(3/6)(3/5)= 0.1714
P(bbb)= (4/7)(3/6)(2/5)= 0.1143
10.4 There are 2 identical urns, so the probability that one urn will yield in one white and one black ball, order unimportant, and the other urn will yield something else = ((3/7)(4/6)+(4/7)(3/6))*(1-((3/7)(4/6)+(4/7)(3/6)))=
(0.5714)*(1-0.5714)= 0.2449