10th Class Mathematics Probability Question Bank MCQs - Probability

The probability of passing a certain test is \[\frac{x}{24}\]. If the probability of not passing it is \[\frac{7}{8},\] then x is equal to:

A) 2

B) 3

C) 4

D) 6

Correct Answer: B

Solution :

[b] Let E be the event 'passing the test'.

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,P(E)=\frac{X}{24}\]

Also, P (not passing the test) \[=P(\bar{E})=\frac{7}{8}\]

Now, \[P(E)+P(\bar{E})=1\]

\[\Rightarrow \,\,\,\,\,\,\frac{x}{24}+\frac{7}{8}=1\Rightarrow \frac{x}{24}=1-\frac{7}{8}\Rightarrow x=\frac{24}{8}=3\]