Question

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

c. for each trial, the probability of outcome a is 0.70; the probability of outcome b is 0.20; and the probability of outcome c is 0.10. suppose there are 10 trials. (a) can we use the binomial experiment model to determine the probability of four outcomes of type a, five of type b, and one of type c

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%