(a) Find the probability that three of them are defective. (Round your answer to four decimal places.)
(b) Find the probability that at least two of them are defective. (Round your answer to four decimal places.)
Answer:
Given Data :
Probability of success $(p)=0.2$
Sample size $(n)=5$
(A) The probability that exactly three are defective:
$P(x = 3) = \binom{n}{x} \cdot p^x \cdot (1 – p)^{n – x} = \binom{5}{3} \cdot 0.2^3 \cdot (1 – 0.2)^{5 – 3} = 0.0512$
(B) The probability that at least two of them are defective :
$P(x \geq 2) = \sum_{2}^{5} \binom{n}{x} \cdot p^x \cdot (1 – p)^{n – x} = \sum_{2}^{5} \binom{5}{x} \cdot 0.2^x \cdot (1 – 0.2)^{5 – x} = 0.2627$
