Binomial distribution exact

probability solution-verification statistics binomial-distribution

Solution 1:

Yes, it is correct, since replacement is allowed, each draw can be viewed as iid Bernoulli trial with probability of success $0.7$. The number of black balls out of $4$ trials is then $Bin(4, 0.7)$.

$$\binom{4}{2}(0.7)^2(0.3)^2=6(0.21)^2=6\left(\frac{21}{100} \right)^2=\frac{2646}{10000}$$

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