Question 200336
You're confusing "and" and "or". With "and", you multiply the probabilities.


a) 


P(Black AND Black) = P(Black) * P(Black)


P(Black AND Black) = (2/5) * (1/4)


P(Black AND Black) = 2/20


P(Black AND Black) = 1/10


P(Black AND Black) = 0.1 which is 10%



So there's a 10% chance that you select both black balls (without replacement)



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b) 



P(Black AND Black) = P(Black) * P(Black)


P(Black AND Black) = (2/5) * (2/5)


P(Black AND Black) = 4/25


P(Black AND Black) = 0.16 which is 16%



So there's a 16% chance that you select both black balls (with replacement)



If you aren't sure about the answers, you can use a smaller sample and draw a tree to display all the possible outcomes (this will help you calculate the probabilities)