Let E denote the random experimnet of rolling two unbiased dice and A and B are two events connected with E. The event A occur if the sum of the digits shown on the two dice is 7 while the event B occurs if at least one of the dice shows up a 4. show that the events A and B neither mutually exclusive nor exhaustive.

If A and B are two mutually exclusive events, then-

Two unbiased dice are thrown .Let A be the event that the sum of the digits shown on the two dice is 5 and B be the event that at least one of the dice shows up a 5. Are the two events i. mutually exclusice? (ii) exhaustive? Give arguments in support of your answer.

If A and B are two mutually exclusive event then P(A-B) =

In the random rxperiment of rolling an unbiased die, let A be the event of getting a digit less than 4 and B be then event of getting a digit greater than 3 , show that the events A and B are mutually exclusive and exhaustive.

Describe the following events A,B, and C in the random experiment of tossing three unbiased coins : A: event of getting two heads, B: event of getting three heads. C: event of getting atmost one head. Show that (i) B is a simple event while A and C are compound events, (ii) events A,B,C are mutually exclusive and exhaustive.

If A and B are two events, then the probability that one and only one event occurs is -

If A and B are two events, then probability that exactly one of them occurs is -

Three unbaised coins are tossed simultaneously. Describe two events A and B which are mutually exclusive,

A die is rolled. Let E be the event "die shows 4" and F be the event "die shows even number". Are E and F mutually exclusive?

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event the sum of numbers on the dice is 4".