Question

In an experiment, there are n independent trials. for each trial, there are three outcomes, a, b, and

Answer 1

The formula for a binomial probability function is the one that is attached to the image.
 Where:
 n = number of trials.
 x = number of successes from which you want to know the probability.
 p = probability of obtaining success.

 In this case, success is defined as obtaining a result of type a.
 We look for the probability of obtaining 4 results of type a.
  So:
 n = 10.
 x = 4.
 p = 0.70.
 In this way:
 P (x = 4) = 0.0368.

 If we now look for the probability of obtaining 5 results of type b.
 So:
 n = 10.
 x = 5.
 p = 0.20.
 P (x = 5) = 0.0264.

 Finally, the probability of obtaining 1 result of type c.
 n = 10.
 x = 1.
 p = 0.1.
 P (x = 1) = 0.387.
 Finally, the probability of obtaining 4 results of type a, 5 of type b and 1 of type c is:
 P (4a + 5b + 1c) = 0.0368 * 0.0264 * 0.387.
 P = 0.0376%