Question

A gambling game pays 4 to 1 and the chance of winning is 1 in 6. Suppose you bet $1 on this game 600 times independently.
Find the expected number of times you win.
Find the SE of the number of times you win.
Find the chance that you lose more than $50 (that is, your net gain in the 600 bets is less than -$50).

Answer 1

expected number of times you win is 100

wins is 1 in 6, total 600.

Answer 2

\[SE=\sqrt(np(1-p))\]

Answer 3

so basically the SE is 9.1287

Answer 4

9.1287 is correct

Answer 5

Find the chance that you lose more than $50 (that is, your net gain in the 600 bets is less than -$50).