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?

A coin is tossed once. If the shows head, it is tossed again and if it shows tail, then a dice is tossed. Let E_1 be the event with first toss results into a tail and E_2 , the event: the dice shows a number greater than 4. find P(E_2//E_1) .

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, ‘the number is even,’ and B be the event, ‘the number is red’. Are A and B independent?

Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the event” three tails show and D denote the event ‘a head shows on the first coin”. Which events are mutually exclusive?

A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.

Two dice are rolled. Let A, B and C be the events of getting a sum 2, a sum 3 and a sum 4 respectively. Are events A and B mutually exclusive ?

Three coins are tossed once. Let A denote the event "three heads show", B denote the event "two heads and one tail show", C denote the event "three tails show and D denote the event "a head shows on the first coin". Which events are (i) mutually exclusive ? (ii) in simple ? (iii) compound ?

Consider the experiment of rolling a die. Let A be the event “getting a prime number, B be the event “getting an odd number.” Write the sets representing the event : A or B.

Consider the experiment of rolling a die. Let A be the event “getting a prime number, B be the event “getting an odd number.” Write the sets representing the event : A and B.

Consider the experiment of rolling a die. Let A be the event “getting a prime number, B be the event “getting an odd number.” Write the sets representing the event : A but not B.