A small college has 800 students, 10 percent of which are left-handed. Suppose we randomly select 8 students, because SRS = 8, and assume L = 3.

Also, assume we have to find the probability that exactly 3 out of the 8 students are left-handed, or the probability that L=3.

We use the binomial distribution for calculating this

^{n}C_{r} \cdot p^{r} (1-p)^{n-r}

p is the probability of successes which is 10% or 0.1, n = 8, r = 3. Plugging these in we get

^{8}C_{3}(0.10)^{3}(1-0.10)^{8-3}

= 56 (0.001)(0.9)^{5}

=0.033

So, the probability of getting 3 lefthanded students is 0.033.

I found an answer from www.khanacademy.org

**Binomial probability** example (video) | Khan Academy

We can use the **binomial distribution** to find the **probability** of getting a certain ...
**Binomial random variables** ... **Binomial** mean and standard deviation **formulas** ...
It may not be exact because this is experimental **data**, but it should be close. ...
**AP**® is a registered trademark of the College Board, which has not reviewed this
...

For more information, see **Binomial probability** example (video) | Khan Academy