List of top Mathematics Questions on Probability asked in Karnataka PGCET

In a cross-sectional study conducted at a clinic, the researcher is interested to know what proportion of the patients is suffering from tuberculosis and HIV.

\[ \begin{array}{|c|c|c|} \hline & \text{Tuberculosis (Yes)} & \text{Tuberculosis (No)} \\ \hline \text{HIV +ve} & 16 & 4 \\ \hline \text{HIV -ve} & 24 & 456 \\ \hline \end{array} \]

The probability that a person selected is not suffering from both tuberculosis and HIV is:

If \(P(A)=0.8\), \(P(B)=0.5\) and \(P(B|A)=0.4\), then the value of \(P(A|B)\) is:
An experiment succeeds twice as often as it fails. The probability of success in the next trial is:
If an event cannot occur, then its probability is:
Two dice are thrown and the sum of the numbers which come up on the dice is noted. Among the following events:
• A: The sum is even.
• B: The sum is a multiple of 3.
• C: The sum is less than 4.
• D: The sum is greater than 11. Which pair of events are mutually exclusive?
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually six.
Three cards are drawn successively without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?
The probability of selecting a man from a crowd containing 20 men and 33 women is
Two students A and B appear for an exam. Probability that A passes is 0.05, B passes is 0.10, and both pass is 0.02. Find probability that neither passes.
Two dice are thrown and the sum of the numbers which come up is noted. Among the following events: A: sum is even, B: sum is multiple of 3, C: sum is less than 4, D: sum is greater than 11. Which pair of events are mutually exclusive?
If the probability of getting Rh+ve is 0.9 and probability of new born being male is \(1/2\), then the probability of new born being male with Rh+ve is
A class of 40 students showed that 20% were taller, 40% were shorter and 40% were shortest. Then the probability that the students are either taller or shortest is?
There is a list of a hospital with admitted patients by age for one day. There were 1000 patients attended. Among these patients, children below 5 years were 600; 200 were between the age of 5 years and 45 years and 200 were above 45 years. Then the proportion of patients attended by the hospital to be of age less than five years and adults of 45 years and above is
Two fair dice are thrown simultaneously. What is the probability of getting a sum of exactly 9?