A) \[\frac{1}{4}\]
B) \[\frac{2}{4}\]
C) \[\frac{3}{4}\]
D) None of these
Correct Answer: A
Solution :
Given, one integer is chosen at random from the first 200 positive integers and integer chosen is divisible by 6 or 8 \[\therefore \] One integer can be chosen out of 200 integers in\[{{\,}^{200}}{{C}_{1}}\]ways. Let A be the event that an integer selected is divisible by 6 and B that it is divisible by 8. Then, \[P(A)=\frac{33}{200},P(B)=\frac{25}{200}\] and \[P(A\cap B)=\frac{8}{200}\] \[\therefore \] \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[=\frac{33}{200}+\frac{25}{200}-\frac{8}{200}=\frac{1}{4}.\]
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