MEDIUM
JEE Main
IMPORTANT
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A person throws two fair dice. He wins Rs. for throwing a doublet (same numbers on the two dice), wins Rs when the throw results in the sum of , and loses Rs. for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:

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Important Questions on Probability
HARD
JEE Main
IMPORTANT
For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is then the probability that he is unable to solve less than two problems is

HARD
JEE Main
IMPORTANT
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

HARD
JEE Main
IMPORTANT
In a class of students, opted for NCC, opted for NSS and opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

HARD
JEE Main
IMPORTANT
In a game, a man wins Rs. if he gets or on a throw of a fair die and loses Rs. for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

MEDIUM
JEE Main
IMPORTANT
A bag contains red and black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

MEDIUM
JEE Main
IMPORTANT
A box contains white, red and black balls. Another box contains white, red and black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box is :

HARD
JEE Main
IMPORTANT
Two different families and are blessed with equal number of children. There are tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family is then the number of children in each family is

HARD
JEE Main
IMPORTANT
Let and be three events, which are pair-wise independent and denotes the complement of an event . If and then is equal to
