A dice is thrown twice. Let A and be the event ,First dice shows 5 and B be the event, second dice shown 3 Find `P(AcupB)`.

A die is thrown twice. Let A be the event, 'First die shows 5' and B be the event, 'second die shows 5'. Find P(A uu B) .

An unbaised die is thrown twice. Let the event A be "odd number on the first throw" and B be the event odd number on the second throw. Check the independence of the events A and B

An unbiased die is thrown twice. Let the event A be 'odd number on the first throw' and B the event 'odd number on the second throw'. Check the independence of the events A and B.

Consider the random experiment of throwing two dice. Let A be the event of getting the sum of11 and B is the event of getting a number other than 5 on the first die. Are A and B independent events?

A dice is thrown. The probability that the first time 1 occurs at the even throw is

A fair die is thrown twice. Let A denote the event that '4' has appeared atleast once. Let B denote the event that the sum of the outcomes in two trials is 6. i Write down the set of favourable outcomes for the event A. ii. Write down the set of favourable outcomes for the events B iii Compute P(A|B), the conditional probabilityof A given B.

Let two fair six-faced dice A and B be thrown simultaneously. If E_1 is the event that die A shows up four, E_2 is the event that die B shows up two and E_3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ? (1) E_1 and E_2 are independent. (2) E_2 and E_3 are independent. (3) E_1 and E_3 are independent. (4) E_1 , E_2 and E_3 are independent.