The probability that at least one detector detects it is 0.027.
What is probability?
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Given,
the probability that smoke detector detect fire = 0.9
the probability that smoke detector doesnot detect fire = 1-0.9 = 0.1
The probability that at least one detect it
we will use combination
C(n, r) = n!/r!(n–r)!,where 0 ≤ r ≤ n
n = 3
r = 1
=3!/2!(0.9)[tex]0.1^{2}[/tex]
=0.027
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