We have six black boxes Bo, BI,. Bs, with box Bi containing i red balls and 5 -

Question

We have six black boxes Bo, BI,. Bs, with box Bi containing i red balls and 5 - i green balls. One box is chosen at random 1. Three balls are drawn from the box with replacement between draws. Given that the drawn balls are red, green and red (in that order exactly), what is the chance that the box B3 was initially chosen? 2. What would your answer to 1. be if you knew that there were two red balls and one green among the three chosen balls (i.e., this time you do not know the order of chosen colours)? 3. What would your answer to 1. be if you knew the draws were made without replace- ment?

Explanation / Answer

Prob of choosing B3 = 1/5

B3 contains 3 red and 2 green balls

P (1st red) = 3/5

P(2nd green) = 2/5

P(3rd red) = 3/5

P(B3 with given order) = 1/5* 3/5*2/5*3/5 = 18/625

(ii)

The answer will still be same because order doesn't matter

(iii)

If no replacement

Prob of choosing B3 = 1/5

B3 contains 3 red and 2 green balls

P (1st red) = 3/5

P(2nd green) = 2/4

P(3rd red) = 2/3

P(B3 with given order) = 1/5* 3/5*2/4*2/3 = 12/300

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