Understanding likelihood

Four events, ordered least to most likely. The scoring is in the two extremes: impossible is 0 and certain is 1, and one of each is usually hiding in the list.

01 Worked Example Video

▸ VIDEO COMING SOON

A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 What This Looks Like on ALEKS

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

Which is impossible?

A bag contains only 7 white and 5 black counters.

What is the probability of drawing a yellow counter? Type just the number.

P =

Which is certain?

A bag contains only 7 white and 5 black counters.

What is the probability of drawing a counter that is white or black? Type just the number.

P =

Counts can mislead

Box A: 4 black and 12 blue pens. Box B: 3 black and 7 blue pens.

Which is more likely: black from A, or black from B? Type A or B.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

every probability sits on \(0 \le P \le 1\) 0 is impossible, 1 is certain, nothing lives outside

an outcome that cannot happen is 0 an outcome covering everything is 1

Work out each probability as a decimal, then sort. The two easy marks are the events you never have to compute: anything asking for a colour that is not in the box is 0, and anything listing every colour that is in the box is 1. Spot those two first and you have often placed the ends of the order without doing arithmetic.

Common slips

(1) Skipped the impossible event. A green pen in a box of black and blue pens is probability 0, not “unlikely”. It goes first. (2) Compared counts instead of probabilities. 4 out of 16 is less likely than 3 out of 10, even though 4 is bigger than 3. (3) Ordered most-to-least. Read which direction the arrow points.

04 Practice — Step by Step

Compute, then sort

Two boxes hold only red and green marbles.

Box A has 5 red and 15 green. Box B has 6 red and 4 green.

One marble is drawn from each box. Order these from least to most likely:

Event 1: drawing red from Box A.
Event 2: drawing blue from Box A.
Event 3: drawing red from Box B.
Event 4: drawing red or green from Box B.

Step 1

The impossible one

Box A holds only red and green. What is the probability of drawing blue?

P =

Step 2

The certain one

Box B holds only red and green. What is the probability of drawing red or green?

P =

Step 3

The two in the middle

Event 1 is 5 out of 20; event 3 is 6 out of 10. Which is larger, 1 or 3?

Q1 Q3

Understanding likelihood

Two free marks every time