total probability

Question

A bag contains 3 balls. Given that one of the balls is red and the other two balls can be either red or non-red..what is the probability of picking up a red ball?

Answer 1

First let's see what are the possibilities for other two balls : 

   RR  ,  NR or RN ( this gives same probability for drawing a Red ball ) , NN

Case 1(RR) :  (Including R it becomes RRR)

       probability of Drawing a red ball here is  1 {As all balls become RED }

       probability of occuring of this case is 1/4   {As other cases can be RN,NR,NN }

    So, Total probability of Drawing a red ball for this case = 1/4 * 1

Case 2(NR or RN) :  (Including R it becomes RNR,RRN)

       probability of Drawing a red ball here is  2/3 {As 2 balls are RED }

       probability of occuring of this case is 2/4   {As other cases can be RR,NN }

    So, Total probability of Drawing a red ball for this case = 2/4 * 2/3

 

Case 3(NN) :  (Including R it becomes RNN)

       probability of Drawing a red ball here is  1/3 {As one ball is RED }

       probability of occuring of this case is 1/4   {As other cases can be RN,NR,RR }

    So, Total probability of Drawing a red ball for this case = 1/4 * 1/3

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Summing up , we get   (1/4 * 1) + (2/4 * 2/3)  + (1/4 * 1/3)  = 2/3

Answer 2

Considering the 2 cases {RRR ,RNN}

case 1 : If the other two balls were red than the probability of picking up a red ball is  1 .

case 2 : If the other two balls were non red the probability of picking up a red ball is 1/3 .

Probability of occurring each of these cases is 0.5

Therefore total probability is (1+ 1/3 ) *.5 = 4/6 = 2/3

Comments

no no...they meant other two balls can be either red or non red...therefore two possibilities for each...

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@Arayana whatever you do probability won't go above 1. In these questions if confused try out the sample space. It is bit ambiguous in question- the possibilities = {RRR, RNN} where R is red and N is non-red. Is this what is meant in question? Now, if we see we need another probability to know which of these is there- assuming equal probability we have to multiply this 0.5 also.

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ok sir i got your point . Assuming {RRR ,RNN} are the given cases i am editing the answer . And @Debanjan if you consider the other cases {RRR, RNN , RNR , RRN } multiply with .25 .