Answer: 0.8025
Step-by-step explanation:
Given : The number of defective calculators : 17
The number of calculators are not defective : 37
Total calculators : 37+17=54
The probability of the calculators are defective : [tex]\dfrac{17}{54}=\dfrac{1}{3}[/tex]
Binomial distribution formula :-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of success in x trials, n is total trials and p is the probability of success for one trial.
The probability that at least one of the calculators is defective is given by :-
[tex]P(x\geq1)=1-P(0)\\\=1-(^4C_0(\dfrac{1}{3})^0(1-\dfrac{1}{3})^4)\\\\=1-(\dfrac{2}{3})^4=0.80246913\approx0.8025[/tex]
