Question

A turn consists of rolling a standard die and tossing a fair coin. The game is won when the die shows a 1 or a 6 and the coin shows heads. What is the probability the game will be won before the fourth turn

Answer 1

0.5021 or about 50%

Explanation:

chance of getting heads is 1 out of 2 =1/2

chance of getting 1or 6 is 2 out of 6 = 2/6

1/2 * 2/6= 2/12 reduced to 1/6

each turn you have a 1 0ut of 6 chance of winning

16% chance of winning so an 84% chance of losing

chance of losing 4 times is .84 ^4 =0.4979

chance of winning is 1-(.84^4)= 0.5021