A roulette wheel has 38 numbers. Eighteen of the numbers
are black, eighteen are red, and two are green. When the wheel is spun,
the ball is equally likely to land on any of the 38 numbers. Each spin
of the wheel is independent of all other spins of the wheel. One
roulette bet is a bet on black—that the ball will stop on one of the
black numbers. The payoff for winning a bet on black is $2 for every $1
one bets; that is, if you win, you get the dollar ante back and an
additional dollar, for a net gain of $1, while if you lose, you gets
nothing back, for a net loss of $1. Each $1 bet thus results in the gain
or loss of $1. Suppose one repeatedly places $1 bets on black, and
plays until either winning $7 more than he has lost, or loses $7 more
than he has won. Equivalently, one plays until the first time that
| net winnings | = | $won - $bet | = |$2×(#bets won) - $1×#bets | = $7,
where |x| is the absolute value of x.
Question 1: The chance that one places exactly 6 bets before stopping is_______
Question 2:The chance that one places exactly 7 bets before stopping is_______
Question 3:The chance that one places exactly 8 bets before stopping is________
Question 4: The chance that one places exactly 9 bets before stopping is_________
Thank you so much!!