Question

q 22.) eddies used autos has cars available with the combinations of colors, engines, and transmissions indicated in the following tree - diagram. what is the probability of choosing a white car with a 4 - cylinder engine and a manual transmission? express your answer as a fraction in simplest form.
color
engine
transmission
blue
6 - cylinder
4 - cylinder
automatic
manual
automatic
manual
red
6 - cylinder
4 - cylinder
automatic
manual
automatic
manual

Explanation:

Step1: Count total outcomes

There are 2 colors (blue and red), for each color there are 2 engine - types (4 - cylinder and 6 - cylinder), and for each engine - type there are 2 transmission - types (automatic and manual). So the total number of outcomes is \(2\times2\times2=8\).

Step2: Count favorable outcomes

We want a white car (not given in the tree, assume no white cars, so we focus on the given colors), a 4 - cylinder engine and a manual transmission. Looking at the tree, for blue and red, when considering 4 - cylinder engines, there is 1 manual - transmission option for each color. So there are \(1 + 1=2\) favorable outcomes.

Step3: Calculate probability

The probability \(P\) is the number of favorable outcomes divided by the number of total outcomes. So \(P=\frac{2}{8}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)