Understanding likelihood
Four events to put in order. Two of them you can place without any arithmetic at all, and spotting those first is most of the question.
A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.
ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.
A box holds only red and green counters: 6 red and 9 green.
What is the probability of drawing a yellow counter? Enter a single number.
The same box: 6 red and 9 green, and nothing else.
What is the probability of drawing a counter that is red or green? Enter a single number.
Jar X: 5 blue, 3 white. Jar Y: 8 blue, 5 white.
Which jar is more likely to give a blue marble? Answer X or Y.
There are two jars containing only blue and white marbles.
Jar A has 7 blue and 3 white.
Jar B has 9 blue and 3 white.
A marble is randomly chosen from each jar. List these events from least likely to most likely.
Event 1: choosing a blue marble from Jar B
Event 2: choosing a blue marble from Jar A
Event 3: choosing a blue or white marble from Jar B
Event 4: choosing a black marble from Jar A
Which event is impossible?
Which event is certain?
Now the middle two: Event 2
And Event 1
Put them in order
Two were free, two were the actual question
Event 4 is impossible and Event 3 is certain, so they bracket the list before any arithmetic happens. That leaves two ordinary fractions, 0.7 and 0.75, and they are close.
That closeness is deliberate. If the middle two were 0.2 and 0.9 you could eyeball it. At 0.7 versus 0.75, comparing the counts (7 blue versus 9 blue) gives the wrong answer, because the jars are different sizes. You have to actually divide.