The following represents the probability distribution of the number of classes a student takes in a spring semester.

x P(x) 1 0.115 2 3 0.422 4 0.312 5 0.034 6 0.015

Find the missing probability.

X        1       2       3         4          5          6

P(X) 0.115   a     0.422   0.312   0.034   0.015

If we want a probability distribution we need to satisfy two important conditions:

1)

2)

And using the second condition we have this:

With a the probability associated with the value of X=2 and solving for a we got:

So then for this case

Step-by-step explanation:

Let X the random variable that represent the number of classes that a student takes

For this case we have the following probability distribution given:

X        1       2       3         4          5          6

P(X) 0.115   a     0.422   0.312   0.034   0.015

If we want a probability distribution we need to satisfy two important conditions:

1)

2)

And using the second condition we have this:

With a the probability associated with the value of X=2 and solving for a we got:

So then for this case