# Binomial Distribution

#### PitaTheGreat

##### New Member
I really need help with this homework. I've been on one question for over an hour.

The Question is The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 17 Southwest flights and observing whether they arrive on time.

(a) Find the probability that exactly 9 flights arrive late.

I came down to it being (17/!17!(17−9)!) *(2^9) *(8)^17−9

But it's getting marked wrong. The steps and answer would be greatly appreciated.

#### PitaTheGreat

##### New Member
I figured it out, the answer is 17C9( .2)^9(.8)^8 = .0020882131

Can anyone explain to me why we do 17C9?

#### PitaTheGreat

##### New Member
If I could get some help on this homework question as well.

The age distribution for senators in the 104th U.S. Congress was as follows:

Under 40: 1
40-49 =14
50-59 = 41
60-69 = 27
70 and older = 17

Consider the following four events:

A = event the senator is under 40
B = event the senator is in his or her 50s
C = event the senator is 40 or older
D = event the senator is under 60

Find P (A and D)

Find (B and D)

#### Dason

I figured it out, the answer is 17C9( .2)^9(.8)^8 = .0020882131

Can anyone explain to me why we do 17C9?
Because there are 17C9 ways in which you can get 9 successes out of 17 trials.

#### PitaTheGreat

##### New Member
Thanks. Now If someone could help with the other question

#### Dason

Can you be a little more specific? Because you're using 'and' but I think you may have meant 'or'. Was the question phrased that way or did it use unions/intersections?

#### PitaTheGreat

##### New Member
It said "and" in the question just like that. Let me post all of what it's asking.

Find P (A and D)

Find (B and D)

Find A or C = 1 (answered this)
Find not D = .44 (answered this)

#### Dason

I probably should have paid more attention to those events actually. Take a look at what it would mean for somebody to be in both A and D. Can you describe that using just one of the sets? What is the probability of that set? Can you do something similar for B and D?

#### PitaTheGreat

##### New Member
Well for B and D i tried B= 41 and D = 56 so .41 x .56 = .2296

It marks that as incorrect.