A man will win $1 if he throws 1,2,3, or 4 and will lose $3 if he throws a 5 or 6 with a single die. If the man will throw a die, what will be his mathematical expectation?
prob(a 1,2,3, or 4) = 4/6 = 2/3
prob(5 or 6) = 1/3
expectations
= (2/3)($1) + (1/3)($3)
= $0.67 + $1
= $1.67