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%
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%