Help Needed for Probability Problem - 2nd Year Economics Student

[tunganhtr]

Hi, I am a 2nd year student in Economics. I have some difficulties with probability. Here is a problem that I cannot solve and I need some help.

It is supposed that only 50% of the students of a sample will go up to the level master. One chooses by chance 18 students.
Which is the probability so that at least 10 go up to the level master.

I want just to know in this exercise, which is the law of probability that one must apply.
Thank you for your assistance, and I'm so sorry for my bad English.

 

[marcmtlca]

$$\Large \sum_{x=10}^{18}(.5)^x(.5)^{18-x}$$

 

[tunganhtr]

Thanks you very much for the answer. It helps me a lot !
:)

 

[HallsofIvy]

tunganhtr, I feel I really should point out to you that marcmtlca's answer is INCORRECT. It doesn't help you as much as you think.

(In fact,
$$\Large \sum_{x=10}^{18}(.5)^x(.5)^{18-x}$$
$$= \Large \sum_{x= 10}^{18}(.5)^{18}$$
$$= 9(.5)^{18}= 0.00004196$$
which is much too small.)

Do you remember why this is called a "binomial" distribution?