if a man has a 10% chance of winning a race and is entered in 6 races, what is the chance he will any race at all?

Question

regardless of wins one race, 2 races, all races etc. simply what is the probability that he wins at all. Assume all equal and one doesnt affect the other.

Answer 1

The probability of winning all 6 races is the combination of a bunch of probabilities: the probability of winning exactly one race, plus the probability of winning exactly two races, plus the probability of winning exactly three races, and so on.

But that's verrrrry messy. The trick here is to realize that there is only one other possible outcome: the man doesn't win any races at all! Either he wins at least one race, or he doesn't win any races. So, together, there's a 100% chance that he either wins at least one race, or he wins no races. If I can figure out the chance that he doesn't win any of them, then the remainder of the 100% is the answer I'm looking for.

- The chance of not winning a race, if I win 10% of the time, would be 90%.

- What are the chances of not winning the first race aaaaand not winning the second race? That's .9 * .9.
- How about not winning three races in a row? That's .9 * .9 * .9.

If you can figure out the chance of not winning all six races, the remaining percentage would tell you how often he has won at least one of the races.

Hope this helps!

Answer 2

Andrew: The man has a 10% chance of winning a race.  If he enters 6 races, you multiply 10% times itself 6 times.  You end up with 1 times 10^-6 .  (.1)(.1)(.1)(.1)(.1)(.1) = .000001.which is 1 in 100,000.  Let's hope that someone else reviews my answer to end up with same probability.  I feel confident this is correct.  Good luck!!