Question

if performances on ap statistics tests are independent and the probability of passing an ap statistics test is 0.2, then the probability of passing three ap statistics tests is:

Explanation:

Step1: Use the multiplication rule for independent events

If two events \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)\times P(B)\). For \(n\) independent events \(E_1,E_2,\cdots,E_n\), \(P(E_1\cap E_2\cap\cdots\cap E_n)=P(E_1)\times P(E_2)\times\cdots\times P(E_n)\)
Let \(P\) be the probability of passing a test. Here \(P = 0.2\) and \(n=3\)
The probability of passing three independent tests is \(P\times P\times P\)

Step2: Calculate the probability

Substitute \(P = 0.2\) into the formula \(P\times P\times P\)
\(0.2\times0.2\times0.2=(0.2)^3\)
\((0.2)^3=\frac{2}{10}\times\frac{2}{10}\times\frac{2}{10}=\frac{8}{1000}=0.008\)

Answer:

\(0.008\) (the green - colored option)