Question

the probability that a car engine will start in the cold is 9/10. whats the probability it will not start once in the next 4 tries? the answer is 9/10 x 9/10 x 9/10 x 1/10 x 4 = 729/2500 but i dont know how

Answer 1

@hpilato Have you studied binomial probabilty?

If so, then you will know that the setup is:

C(4,1) * (1/10)^1 * (9/10)^3 = 729/2500.

Answer 2

You can also write out how the one not start could happen.

N for not start
Y for start

NYYY = (1/10) * (9/10) * (9/10) * (9/10) = ?
YNYY
YYNY
YYYN

Get each probability and add all four results. You should get the correct answer.