# help i need somebody!!

#### kevdhero

##### New Member
The probability that a flight from a certain airline arrives on time is 0.8. Find the probability that in a random sample of 12 flights:
Question 1 : Exactly 10 of the flights were on time.
Question 2 : At least 10 of the flights were on time.
Question 3 : At most 10 of the flights were on time.

any help wud be greatly appreciated!
i think its (.8)^10 for the first one or something like that but i'm prob wrong..

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#### kazec

##### New Member
(0.8)^10 is a good start, but it's wrong.

Should have been 0.8^10*0.2^2*(12, 10)

Where (x, y) is combination number.

You can try to work out the rest.

#### kevdhero

##### New Member
What do you mean by combination number, not familiar with that notation! thanks!

attempted other 2 questions... .
0.8)^10
1-(.2)^2

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#### IronMan

##### New Member
You need to use the binomial distribution to get the probabilities correct I think.

#### kazec

##### New Member
(x, y) = number of different ways of picking y marbles from a total of x marbles.

(12, 10) = (12, 2) = 12*11/(2*1) = 66

===================================================

For question (2),

At least 10 on time = at most 2 not on time

so P = 1-P(0 not on time)-P(1 not on time)-P(2 not on time) = ...

===================================================

For question (3)

At most 10 on time = number of on-time planes <= 10 ---> P1
At least 10 on time = number of on-time planes >= 10 ---> P2

P1+P2-P(number of on-time planes = 10) = 1

So P1 = 1+P(number of on-time planes = 10)-P2

where the quantities on the right-hand side you worked out in questions (1) and (2).