Answer with Step-by-step explanation:
In case of Bernoulli trails
The probability that a random variable occurs 'r' times in 'n' trails is given by
[tex]P(E)=\binom{n}{r}p^r(1-p)^{n-r}[/tex]
where
'p' is the probability of success of the event
Part a)
probability that no contamination occurs can be found by putting r = 0
Thus we get
[tex]P(E_1)=\binom{5}{0}0.1^0(1-0.1)^{5}=0.5905[/tex]
part b)
The probability that at least 1 contamination occurs is given by
[tex]P(E)=1-(1-p)^{n}[/tex]
Applying values we get
[tex]P(E_2)=1-(1-0.1)^{5}=0.4096[/tex]
