A black and a blue die are rolled (both fair and six sided). What is the probability that the sum of their numbers is 5 and that the number on the blue die is larger than the number on the black die?

Let A be the event that the number on the blue die is larger than the number on the black die, and let B be the event that the sum is 5. Are A and B independent events?

From a normal deck of cards (52 cards altogether), two cards are drawn at random (without replacement). What is the probability of drawing at least one ace?

A bag consists of 2 blue, 5 green and 5 red balls. At random 3 balls are picked out of the bag one by one and without replacement. Compute the probability of picking at least 2 green balls.

Question 3

A farmer from Buckingham has gone duck hunting. When she fires her gun at a duck, the probability of a hit is 18 . On a typical duck hunt the farmer will fire her gun 45 times. Let X denote the number of shots hitting a duck on a typical hunt.

Assuming the shots are fired independently, explain what distribution X

will follow.

What is the probability that at least 10 of the farmer's shots are hits?

What is the probability that the farmer scores between 5 and 15 hits, both included?

What is the probability that the farmer achieves at least one hit?