Probability that I win more than three dollars. There are three slot machines. The prize money in each is 1,2,3 dollars respectively; The probability of winning in respective slot machines is 0.1, 0.4, 0.7 respectively. What is the probability that I will win at least three dollars.? I have to play them in the order they are given and there is no cost of playing.

Note that winning in the third game, you got at least \$3. So, the outcomes you're interested in are

1. victory in the third game: $0.7$,
2. loss in the third game, but victory in the first two: $0.1 \cdot 0.4 \cdot (1-0.7)$.



Your answer is the sum of the two cases, i.e. $0.712$.