# In a large population of high school students, 20% have experienced math anxiety. If you take a random sample of 10 students from this population, what is the probability that exactly two students have experienced math anxiety?

Feb 4, 2017

Probability that exactly two students have experienced math anxiety

${p}_{\left(x = 2\right)} = 0.3$

#### Explanation:

Probability of a randomly chose student to have maths anxiety =20% or 0.2

$p = 0.2$
Then -
$q = 1 - p$
$q = 1 - 0.2 = 0.8$
Probability that exactly two students have experienced math anxiety

${p}_{\left(x\right)} {=}_{n} {C}_{x} \cdot {p}^{x} \cdot {q}^{n - x}$
${p}_{\left(x = 2\right)} {=}_{10} {C}_{2} \cdot {0.2}^{2} \cdot {0.8}^{10 - 2}$
${p}_{\left(x = 2\right)} = 45 \cdot 0.04 \cdot 0.1678$
${p}_{\left(x = 2\right)} = 0.3$

Note: Value of $_ 10 {C}_{2}$ is calculated from calculator