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

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation: