Find the probability of a 4 turning up at least once in two tosses of a fair die.

A die is thrown 6 times. If ‘getting an even number’ is a success, find the probability of getting

(i) exactly 5 successes

(ii) at least 5 successes

(iii) at most 5 successes

A die is thrown 4 times. ‘Getting a 1 or a 6’ is considered a success, Find the probability of getting

(i) exactly 3 successes

(ii) at least 2 successes

(iii) at most 2 successes

A pair of dice is thrown 4 times. If ‘getting a doublet’ is considered a success, find the probability of getting 2 successes.

A pair of dice is thrown 7 times. If ‘getting a total of 7’ is considered a success, find the probability of getting

(i) no success

(ii) exactly 6 successes

(iii) at least 6 successes

(iv) at most 6 successes