Answer that green numbers and number out out red number less than
_____________________________________________________________________________________________________
Given that
= 2/38
= 1/19
P (a red number less than 10)
P(an even black )
18 even black out of 38
= npq
p = probability of success
q = 1 - 1 / 19
1 = 18 / 19
n = 1500 = sample size
p1 = proportion of sample = 77 %
test statistic is
z = [ p1 - p2 / root p(1-p){1/n1 + 1 /n2} ]
= 0.76
z = 0.02 / (0.76*0.24)* (2/1500) 1/2
= 0.0998 from standard normal table
here pvalue is > , proportional = 0.05
When a very large number of rolls, i.e. 10000, in this case, the exact amount of rolls of each number tends to converge its expected value.
10 | 11 | 12 |
---|---|---|
3/36 | 2/36 | 1/36 |
Hence,
Expected Pay-off $1.166667 * 10.000= $11,666.67
Expected \ Pay-off = -\$0.638889*10,000=-\$6,388.89