Answer:
a) Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25
For this case the probability mass function would be given by:
b)
And adding the values we got:
c)
And we can find the individual probabilities:
Step-by-step explanation:
Previous concepts
The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"
Let X the random variable that measures the number of trials until the first success, we know that X follows this distribution:
Part a
Our random variable X="number of tests taken until the individual passes" follows a geomteric distribution with probability of success p=0.25
For this case the probability mass function would be given by:
Part b
We want this probability:
We find the individual probabilities like this:
And adding the values we got:
Part c
For this case we want this probability:
And we can use the complement rule like this:
And we can find the individual probabilities: