List of top Mathematics Questions on Probability asked in COMEDK UGET

An unbiased die is tossed twice. What is the probability of getting a 4, 5 or 6 on the first toss and a 1, 2, 3 or 4 on the second toss?
A pot contains 5 red and 2 green balls. A ball is drawn at random from this pot. If a drawn ball is green, then a red ball is added to the pot. If a drawn ball is red, then a green ball is added to the pot, while the original ball drawn is not replaced in the pot. Now a second ball is drawn at random from the pot, what is the probability that the second ball drawn is a red ball?
In a game, a man wins \( ₹1000 \) if he gets an even number greater than or equal to 4 on a fair dice and loses \( ₹200 \) for getting any other number on the dice. If he decides to throw the dice until he wins or maximum of three times, then his expected gain/loss in \( ₹ \) is -----------
If \( A \) and \( B \) are two events such that \( P(A) = 0.3, P(B) = 0.4, P(A \cap \bar{B}) = 0.5 \), then find the value of \( P(B \cap \bar{A}) \)
Two numbers are selected at random from integers 1 to 9. If their sum is even, what is the probability that both the numbers are odd?
Five persons entered the lift cabin on the ground floor of an eight-floor apartment. Suppose that each of them independently and with equal probability, can leave the cabin at any floor beginning with the first floor, then the probability of all five persons leaving at different floors is:
Let \(A\) and \(B\) be two events such that one of the two events must occur. Given that the chance of occurrence of \(A\) is \( \frac{2}{3} \) the chance of occurrence of \(B\), then odds in favour of \(B\) is
A person writes four letters and addresses four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is
Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?