You watch a roulette wheel spin 270 consecutive times and the ball lands on a red slot each time. what is the probability that the ball will land on a red slot on the next spin

18/37 if you're in Europe, 9/19 if you're in America, assuming the wheel isn't rigged. If the roulette wheel is a fair wheel, the odds on any given spin of the wheel is unaffected by any previous spins of the wheel. So no matter how many times the wheel has consecutively come up red, the next spin can still come up red, black, or green based upon the number of each color is present on the wheel. The difference between the odds for Europe vs America has to do with a quirk about roulette. In Europe, the roulette wheel has 37 slots, 18 red, 18 black, and 1 green. In America, the roulette wheel has 38 slots, 18 red, 18 black, and 2 green. Although in this case, I'd be wary about assuming that the wheel isn't rigged. The odds of 270 consecutive red on a fair wheel is only 1 in 3.09663x10^84 in Europe, or 1 in 4.14949x10^87 in America.

(m+11n)^2=(m+11n)(m+11n)=m^2+11mn+11mn+121n^2=m^2+22mn×121n^2 for example; use foil: (a+b)(a+b)first. a^2outside. abinside. ablast. b^2