A die is thrown three times. Events `A` and `B` are defined as below: A: 4 on the third throw B: 6 on the first and 5 on the second throw, Find the probability of A given that B has already occurred.

(b)three dice are thrown together.Find the probability of getting a total of atleast 6.

An unbiased die is thrown twice. Let A be the event '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

A die is thrown twice let the event A be 'odd number on first throw' and B be 'odd number on the second throw' check whether A and B are independent.

A box contains 30 defective bulbs and 30 non-defective bulbs. Two bulbs are drawn at random. The event A and B are defined as follows. A:'first bulb is defective.' B: 'the second bulb is non defective.' Find probability of A and B. prove that A and B are independent events.

An unbiased die is thrown twice. Let the event A be getting prime number in the first throw and B be the event of getting an even number in the second throw. Check the independence of the events A and B

A and B throw a die alternately till one of them gets a ‘6’ and wins the game. If A stars first, then the probability of winning of A is

Two persons A and B throw a die alternatively till one of them gets a three and wins the game.If A begins,find (ii) the probability of winning of B.

Two persons A and B throw a die alternatively till one of them gets a three and wins the game.If A begins,find (i) the probability of winning of A.

Determine P(E|F). A die thrown three times, E: '4 appears on the third toss .F:'6 and 5 appears respectively on the two tosses'.

A die is thrown again and again until three sixes are obtainined.find the probability of obtaining the third six in the sixth throw of the die.