Question

Construct the probability distribution if three cellphones were to be tested, consider the random variable (x) as the number of defected cellphones.

Answer 1

Let's denote probability that phone is defected as $p$. Then, it's the binomial distribution:

$Pr(x=k)= \binom{3}{k} p^{k} \cdot(1-p)^{3-k},$ where $k$ denotes number of defected phones.

Thus:

$Pr(x=0)= \binom{3}{0} p^{0} \cdot(1-p)^{3-0} = (1-p)^{3}$

$Pr(x=1)= \binom{3}{1} p^{1} \cdot(1-p)^{3-1} = 3 \cdot p \cdot (1-p)^{2}$

$Pr(x=2)= \binom{3}{2} p^{2} \cdot(1-p)^{3-2} = 3 \cdot p^{2} \cdot (1-p)$

$Pr(x=3)= \binom{3}{3} p^{3} \cdot(1-p)^{3-3} = 3 \cdot p^{3}$