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A bag contains 5 balls. Two balls are drawn and are found to be white. What is the probability that all the balls are white? |
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Answer» Correct Answer - `1//2` Let `A_(i)(i=1,2,3,4)` be th eevent that the urn contains `2,3,4 or5` white balls and E the event that two white balls are drawn. Since the four events `A_(1),A_(2),A_(3),A_(4)` are equally likely, therefore `P(A_(i))=1//4,i=1,2,3,4.` Now, the probability tyhat the urn contains 2 white balls and both have been drawn is `P(E//A_(1))=(""^(2)C_(2))/(""^(5)C_(2))=1/10` Similarly, `P(E//A_(2))=(""^(3)C_(2))/(""^(5)C_(2))=3/10,` `P(E//A_(3))=(""^(4)C_(2))/(""^(5)C_(2))=3/5` `P(E//A_(4))=(""^(5)C_(2))/(""^(5)C_(2))=1` Hence, the required probability is `P(A_(4)//E)=(P(A_(4))P(E//A_(2)))/(underset(i=1)overset(4)sumP(A_(i))P(E//A_(i)))` `=(1/4xx1)/(1/4((1)/(10)+(3)/(10)+(3)/(5)+1))=1/2` |
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