Question

A small college has 800 students, 10%, percent of which are left-handed. Suppose they take an SRS of 444 students. Let X= equals the number of left-handed students in the sample.
What is the probability that exactly 2 of the 4 students are left-handed?
You may round your answer to the nearest hundredth.

Answer 1

Probability that exactly 2 of the 4 students are left-handed = 0.02178

Step-by-step explanation:

We have , A small college has 800 students, 10%, percent of which are left-handed. Suppose they take an SRS of 444 students. Let X= equals the number of left-handed students in the sample. We have to find probability that exactly 2 of the 4 students are left-handed . Number of left handed students  = $\frac{800(10)}{100} = 80$  . Now, probability that a student is left handed out of sample of 444 students is  = $\frac{Left-handed-students}{Total-students}$ i.e.

Probability that a student is left handed out of sample of 444 students  = $\frac{80}{444}$ and, Probability that a student is right handed out of sample of 444 students = $1 - \frac{80}{444}$ .

∴ Probability that exactly 2 of the 4 students are left-handed = Probability of (left handed × left handed × right handed × right handed)

Probability that exactly 2 of the 4 students are left-handed = $\frac{80}{444} (\frac{80}{444} )(1-\frac{80}{444} )(1-\frac{80}{444} )$

Probability that exactly 2 of the 4 students are left-handed = 0.02178