Question

You roll a die, winning nothing if the number of spots is odd, $1 for a 2 or a 4, and $10 for a 6.

Answer 1

Answer:  The expected value is 1/6 * 1/2 * 1/3 = 1/36  the standard deviation of 1/36 = 99.7% = 1/36 * 0.997 = 0.0276944444

The mean playing twice = 1/9 =0.111111111

Step-by-step explanation:

to win $10 in one throw = 1/6   to win $1   in one throw =  2/6  and to lose is 1/2  so we have 3 probabilities  and 3(3)= 9 probability combinations = 1/2 to lose  1/3 to win $2  and 1/6 to win $10  playing twice = 1/6 * 1/6 = 1/36  or 1/6* 1/2= 1/12 or 1/6 * 1/3 = 1/18  or 1/2 * 1/2 = 1/4  or 1/2 * 1/6 = 1/12 or 1/2 * 1/3 = 1/6  or 1/3 * 1/3 = 1/9 or 1/3 * 1/2 = 1/6 or 1/3 * 1/6 = 1/18    we write a list  1/36+1/12+1/18+1/4+1/12+1/6+1/9+1/6+1/18  /9 = 34/36 + 2/36 = 36/36 = 1   and 1/9 =0.111111111