q 22.) eddies used autos has cars available with the combinations of colors, engines, and transmissions…

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.\ncolor\nengine\ntransmission\nblue\n6 - cylinder\n4 - cylinder\nautomatic\nmanual\nautomatic\nmanual\nred\n6 - cylinder\n4 - cylinder\nautomatic\nmanual\nautomatic\nmanual

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.\ncolor\nengine\ntransmission\nblue\n6 - cylinder\n4 - cylinder\nautomatic\nmanual\nautomatic\nmanual\nred\n6 - cylinder\n4 - cylinder\nautomatic\nmanual\nautomatic\nmanual

Answer

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})