1. A box contains 5 red balls, 10 blue balls and 5 yellow balls. Consider the fo

Question

1. A box contains 5 red balls, 10 blue balls and 5 yellow balls. Consider the following experiment. Four balls will be selected at random, without replacement from the box (the balls will be selected one at a time). The color of each selected ball will be observed. Moreover, if the selected ball is red or vellow, 3 new balls of the same color will be put in the box If the selected ball is blue, no balls will be added to the box Obtain the probability that the first two balls are red) and the third ball will be blue, and the fourth ball will be yellow

Explanation / Answer

P(first ball is red) =(5/20)

P(second ball red|first ball red) =7/22 (as if first ball red ; 4 red remain and including 3 new red total 7 red and total number of balls =20-1+3=22)

P(third blue|first 2 balls red) =10/24

P(4th ball yellow|first 2 balls red ; 3rd blue) =5/23

P(first two are red ; 3rd blue and 4th will be yellow) =(5/20)*(7/22)*(10/24)*(5/23) =0.007205

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