At a certain casino, there is a gambling game where balls of equal weights are numbered from 1 to 15, placed inside a ta

[answerhappygod]

At a certain casino, there is a gambling game where balls of
equal weights are numbered from 1 to 15, placed inside a tambiolo,
and mixed up. Three balls are selected at random without
replacement, one after the other in succession.
(a) A certain casino patron, Mr. Lee has enough money only to play
a total of 4 bets for the night. Mr. Lee always bets that the
outcome will be such that among the 3 balls selected,
the lowest number is a number lower than “6”. After a streak
of bad luck, what is the probability that Mr. Lee will finally be
lucky and win on the 4th bet?
(b) Another casino patron, Mr. Lewis has enough money to keep
playing the game until he has won 7 bets. If Mr. Lewis always bets
that the outcome will be such that among the 3 balls selected,
there are no consecutive numbers, what is the probability that he
places a total of at most 12 bets?
(c) Another casino patron, Ms. Lane has enough money to keep
playing the game until she has won 5 bets. If Ms. Lane bets that
the outcome will be such that exactly two of the three numbered
balls are perfect squares, what is the probability she places at
least 10 bets?