The probability that a randomly selected two digit positive integer will be a multiple of 11 is [tex]\bold{\frac{1}{10}}[/tex]
Solution:
Number of sample space n(S):
Total number of two digit positive integers = 90
Favorable event P(A):
Two digit multiples of 11 = [tex]\bold{(11, 22, 33, 44, 55, 66, 77, 88, 99)}[/tex]
Number of favorable outcome n(A):
Total number of two digit multiples of 11 = 9
Let us consider the requires probability as P(A); number of favorable outcomes as n(A) and the number of sample space as n(S).
The probability formula is as follows,
[tex]$P(A)=\frac{\text { n(A)}}{\text { n(S) }}[/tex]
On substituting the values in the above formula we get,
[tex]$\Rightarrow P(A)=\frac{9}{90}[/tex]
On simplifying the above equation we get,
[tex]$\Rightarrow P(A)=\frac{1}{10}[/tex]
The required probability is [tex]\bold{\frac{1}{10}}[/tex]
