Probability of <3 Errors in 10-char Msg

[magnifik]

In sending 10 characters, a character error occurs independently with probability 1/10. What is the probability that in a 10-character message, less than 3 errors occur?

I am using the binomial formula (n choose k)p^k(1-p)^n-k where n = 10, p = 1/10, and k is the number of errors. Since the problem statement says less than 3 errors occur, I adding up the values for k = 0, 1, 2

(10 choose 0)(1/10)⁰(1-1/10)¹⁰ + (10 choose 1)(1/10)¹(1-1/10)⁹ + (10 choose 2)(1/10)²(1-1/10)⁸, but i am wondering if I am doing this correctly? should i be adding or multiplying?

 

[Ray Vickson]

In sending 10 characters, a character error occurs independently with probability 1/10. What is the probability that in a 10-character message, less than 3 errors occur?

I am using the binomial formula (n choose k)p^k(1-p)^n-k where n = 10, p = 1/10, and k is the number of errors. Since the problem statement says less than 3 errors occur, I adding up the values for k = 0, 1, 2

(10 choose 0)(1/10)⁰(1-1/10)¹⁰ + (10 choose 1)(1/10)¹(1-1/10)⁹ + (10 choose 2)(1/10)²(1-1/10)⁸, but i am wondering if I am doing this correctly?

You have written everything correctly, so if you have not made any arithmetical errors your answer should be correct.

RGV

 

[magnifik]

thanks