An individual repeatedly attempts to pass a driving test. Suppose that the probability of passing the test with each attempt is 0.25, and that the results of successive tests are independent. Let X be the number of tests taken until the individual passes (a) Find the probability mass function of X (b) Evaluate the probability of passing the test with three or less attempts. (c) Evaluate the probability of passing the test with five or more attempts.

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:

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)