Question

a group of 200 teenagers took a driving test.
before the test, some took a particular drivers education class, and the rest did not.
the results are reported in the following two-way frequency table.

\

$$\begin{tabular}{|c|c|c|} \\hline & failed test & passed test \\\\ \\hline did not take the class & 65 & 75 \\\\ \\hline took the class & 27 & 33 \\\\ \\hline \\end{tabular}$$

a teenager is chosen at random from the group.
complete the following. write your answers as decimals.

(a) find the probability that the teenager passed the test.
\\(p(\text{passed}) = \\)

(b) find the probability that the teenager passed the test, given that she took the class.
\\(p(\text{passed} \mid \text{class}) = \\)

(c) is there evidence that a teenager who takes the class is more likely to pass the test than a randomly chosen teenager from the group?

yes, because the probability found in part (b) is much greater than the probability found in part (a).
no, because the probability found in part (b) is much greater than the probability found in part (a).
yes, because the probability found in part (a) is much greater than the probability found in part (b).
no, because the probability found in part (a) is much greater than the probability found in part (b).
yes, because the probability found in part (b) is about the same as the probability found in part (a).
no, because the probability found in part (b) is about the same as the probability found in part (a).

Explanation:

Calculate the overall probability of passing the test

$$
LATEXBLOCK0
$$

Calculate the conditional probability of passing given taking the class

$$
LATEXBLOCK1
$$

Compare the probabilities to evaluate the evidence

$$
LATEXBLOCK2
$$

Answer:

Question (a)

Find the probability that the teenager passed the test.
\(P(\text{passed}) =\) <blank>0.54</blank>

Question (b)

Find the probability that the teenager passed the test, given that she took the class.
\(P(\text{passed} \mid \text{class}) =\) <blank>0.55</blank>

Question (c)

Is there evidence that a teenager who takes the class is more likely to pass the test than a randomly chosen teenager from the group?

• Yes, because the probability found in part (b) is much greater than the probability found in part (a).
• No, because the probability found in part (b) is much greater than the probability found in part (a).
• Yes, because the probability found in part (a) is much greater than the probability found in part (b).
• No, because the probability found in part (a) is much greater than the probability found in part (b).
• Yes, because the probability found in part (b) is about the same as the probability found in part (a).
• No, because the probability found in part (b) is about the same as the probability found in part (a). (Correct answer)