EASY
Earn 100

Two fair dice are rolled. Let be the event that the first die shows an even number and be the event that the second die shows an odd number. The two events and are:
(a)Mutually exclusive
(b)Independent
(c)Dependent
(d)None of these

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Important Questions on Probability
HARD
Let be two independent events. The probability that happen is and the probability that neither nor happens is , then a value of is:

MEDIUM
In a class, % of students study Maths and Science and % of students study Maths. What is the probability of a students studying Science given the student is already studying Maths?

EASY
If and are any two events such that , then

HARD
One ticket is selected at random from tickets numbered . Then, the probability that the sum of the digits on the selected ticket is , given that the product of these digits is zero, equals

EASY
For the events and then

HARD
Let and be any two events with positive probabilities
Statement I:
Statement II:

EASY
If and are two events such that and , then

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

EASY
The probability that a person will develop immunity after vaccination is If people are given the vaccine then probability that all develop immunity is equal to

HARD
Let two fair six-faced dice and be thrown simultaneously. If is the event that die shows up four, is the event that die shows up two and is the event that the sum of numbers on both dice is odd, then which of the following statements is not true?

EASY
An urn contains red and green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

HARD
If and are any two events such that and then the conditional probability, where denotes the complement of , is equal to :

HARD
Let and be two events such that and where stands for the complement of the event . Then the events and are

MEDIUM
A problem in mathematics is given to three students and their respective probability of solving the problem is and , the probability that the problem will be solved is

MEDIUM
Four persons can hit a target correctly with probabilities and respectively. If all hit at the target independently, then the probability that the target would be hit, is

MEDIUM
Let and be two non-null events such that Then, which of the following statements is always correct?

EASY
A coin is tossed and a die is rolled. The probability that the coin shows head and the die shows is

MEDIUM
If a fair coin is tossed times, the probability that heads does not occur two or more times in a row is

HARD
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 :

