Probability of at least one fall in ten rides

[bjgawp]

Homework Statement

On average a certain jockey falls from her horse once in every 10 rides. What is the probability that she will fall from her horse at least once in the next ten rides?

Homework Equations

Answer is 0.651.

The Attempt at a Solution

I've no idea .. I thought of adding up the probabilities of the jockey falling once, twice, thrice, etc. but that just gives me an answer greater than 1 which would not make sense.

P(Fall at least once) = (1/10) + (1/10 + 1/10) + (1/10 + 1/10 + 1/10) + ...
= 55/10

 

[cristo]

You want to add up the probability that the jockey falls once out of the ten jumps+ the probability that the jockey falls twice out of the ten +... The probability that the jockey falls once is equal to 0.1*0.9*0.9*...*0.9 (where there are nine 0.9's).

Summing this for all the possibilities (i.e. 1 to 9 falls) will give the answer. However, can you see a quick way of doing this? What must the sum of the probability of all the choices (i.e. falls no times, falls once, falls twice...) be?