MEDIUM
JEE Main/Advance
IMPORTANT
Earn 100

Two buses and are scheduled to arrive at a town central bus station at noon. The probability that bus will be late is and the probability that bus is late is and the probability that the bus is late given that bus is late is . Then,
(a)probability that neither bus will be late on a particular day is
(b)probability that bus is late given that the bus is late is
(c)probability that at least one bus is late is
(d)probability that at least one bus is in time is

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Important Questions on Probability II
MEDIUM
JEE Main/Advance
IMPORTANT
A fair coin is tossed times. Let be the number of times heads occurs. Then is maximum when is,

HARD
JEE Main/Advance
IMPORTANT
The probability of choosing an integer out of integers is inversely proportional to . If is the probability that chosen number is odd and is the probability that chosen number is even, then

HARD
JEE Main/Advance
IMPORTANT
A lot contains defective and non-defective bulbs.Two bulbs are drawn at random, one at a time, with replacement.The events are defined as follows:
(first bulbs is defective)
(second bulb is non-defective)
(two bulbs are both defective or both non-defective)
Then,

HARD
JEE Main/Advance
IMPORTANT
If two loaded dice each have the property that or is three times as likely to appear as or on each roll. When two such dice are rolled, the probability of obtaining a total of is , then the value of is, where represents the greatest integer less than or equal to

MEDIUM
JEE Main/Advance
IMPORTANT
An urn contains three red balls and white balls. Mr. draws two balls together from the urn. The probability that they have the same colour is .Mr. draws one balls from the urn, notes its colour and replaces it. He then draws a second ball from the urn and finds that both balls have the same colour is . The possible value of is______________.

EASY
JEE Main/Advance
IMPORTANT
Suppose and are two events with and Let if and are mutually exclusive and if and are independent events, then the value of is,

HARD
JEE Main/Advance
IMPORTANT
Thirty-two players ranked to are playing in a knockout tournament. Assume that in every match between any two players, the better ranked player wins. The probability that ranked and ranked players are winner and runner up respectively is then the value of is, where represents the greatest integer function,

EASY
JEE Main/Advance
IMPORTANT
If and are two events such that and if the greatest value that can have is then the value of is,
