Probability involving choosing from objects that are not distinct

Objects grouped by colour rather than individually labelled. Count the outcomes that satisfy the condition, put it over the total, and leave it as a fraction.

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.

Crayons

A box holds 12 red, 5 blue and 7 yellow crayons.

One is chosen at random. What is the probability it is blue or yellow? Write your answer as a fraction.

P =

A larger set

A drawer holds 14 black, 3 grey and 8 white socks.

One is pulled out at random. What is the probability it is grey or white? Write your answer as a fraction.

P =

Most of the set

A bin holds 4 green, 11 orange and 10 purple tokens.

One is drawn at random. What is the probability it is orange or purple? Write your answer as a fraction.

P =

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

\(P = \dfrac{\text{outcomes that count}}{\text{total outcomes}}\) the same definition as always

or between exclusive groups → add the counts blue or yellow means blue + yellow on the top

Nothing changes because the objects are not individually distinguishable. A box of 12 red, 5 blue and 7 yellow crayons has 24 equally likely draws; you just happen to count them in groups. Add the groups the question asks for, put that over 24, and simplify.

Common slips

(1) Used the number of colours as the total. The denominator is 24 crayons, not 3 colours. (2) Forgot to add the second group. “Blue or yellow” needs both counts on top. (3) Left it unsimplified when a fraction was asked for. ALEKS usually wants the answer as a fraction, so reduce it.

04 Practice — Step by Step

Count, add, divide

A jar holds 9 red, 6 blue and 5 yellow beads.

One bead is drawn at random. What is the probability it is blue or yellow? Write your answer as a fraction.

Step 1

The total

How many beads are there altogether?

Step 2

The outcomes that count

How many beads are blue or yellow?

Step 3

The probability

Write it as a fraction.

P =

Exam 3 Review Q2

Probability involving choosing from objects that are not distinct

Why nothing special is going on